Solve 200000-x=x*[1-1/(1+0.06div12)^69/0.005]

$$200000 - x = x \times [ \frac { 1 - \frac { 1 } { ( 1 + 0.06 \div 12 ) ^ { 69 } } } { 0.005 } ]$$

Solve for x

$$x = \frac{166555108488503064587609001029332426562160727926862970580863751454627545335807046743977681218196177274422806391316638988434037714811807205763370063156169170760200000}{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001} = 3376\frac{2.134315422885035 \times 10^{160}}{4.932872195920445 \times 10^{160}} \approx 3376.432671948$$

Steps for Solving Linear Equation

Expand \frac{0.06}{12} by multiplying both numerator and the denominator by 100.

$$200000-x=x\times \frac{1-\frac{1}{\left(1+\frac{6}{1200}\right)^{69}}}{0.005}$$

Reduce the fraction \frac{6}{1200} to lowest terms by extracting and canceling out 6.

$$200000-x=x\times \frac{1-\frac{1}{\left(1+\frac{1}{200}\right)^{69}}}{0.005}$$

Add 1 and \frac{1}{200} to get \frac{201}{200}.

$$200000-x=x\times \frac{1-\frac{1}{\left(\frac{201}{200}\right)^{69}}}{0.005}$$

Calculate \frac{201}{200} to the power of 69 and get \frac{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$200000-x=x\times \frac{1-\frac{1}{\frac{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}}{0.005}$$

Divide 1 by \frac{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by multiplying 1 by the reciprocal of \frac{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$200000-x=x\times \frac{1-1\times \frac{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}}{0.005}$$

Multiply 1 and \frac{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801} to get \frac{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}.

$$200000-x=x\times \frac{1-\frac{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}}{0.005}$$

Subtract \frac{590295810358705651712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801} from 1 to get \frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}.

$$200000-x=x\times \frac{\frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}}{0.005}$$

Express \frac{\frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}}{0.005} as a single fraction.

$$200000-x=x\times \frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801\times 0.005}$$

Multiply 832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801 and 0.005 to get 4163877712212576614690225025733310664054018198171574264521593786365688633395176168599442030454904431860570159782915974710850942870295180144084251578904229269.005.

$$200000-x=x\times \frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{4163877712212576614690225025733310664054018198171574264521593786365688633395176168599442030454904431860570159782915974710850942870295180144084251578904229269.005}$$

Expand \frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{4163877712212576614690225025733310664054018198171574264521593786365688633395176168599442030454904431860570159782915974710850942870295180144084251578904229269.005} by multiplying both numerator and the denominator by 1000.

$$200000-x=x\times \frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801000}{4163877712212576614690225025733310664054018198171574264521593786365688633395176168599442030454904431860570159782915974710850942870295180144084251578904229269005}$$

Reduce the fraction \frac{242479732083809671226045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801000}{4163877712212576614690225025733310664054018198171574264521593786365688633395176168599442030454904431860570159782915974710850942870295180144084251578904229269005} to lowest terms by extracting and canceling out 5.

$$200000-x=x\times \frac{48495946416761934245209001029332426562160727926862970580863751454627545335807046743977681218196177274422806391316638988434037714811807205763370063156169170760200}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}$$

Subtract x\times \frac{48495946416761934245209001029332426562160727926862970580863751454627545335807046743977681218196177274422806391316638988434037714811807205763370063156169170760200}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801} from both sides.

$$200000-x-x\times \frac{48495946416761934245209001029332426562160727926862970580863751454627545335807046743977681218196177274422806391316638988434037714811807205763370063156169170760200}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}=0$$

Combine -x and -x\times \frac{48495946416761934245209001029332426562160727926862970580863751454627545335807046743977681218196177274422806391316638988434037714811807205763370063156169170760200}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801} to get -\frac{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}x.

$$200000-\frac{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}x=0$$

Subtract 200000 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}x=-200000$$

Multiply both sides by -\frac{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}, the reciprocal of -\frac{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}.

$$x=-200000\left(-\frac{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}\right)$$

Multiply -200000 and -\frac{832775542442515322938045005146662132810803639634314852904318757273137726679035233719888406090980886372114031956583194942170188574059036028816850315780845853801}{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001} to get \frac{166555108488503064587609001029332426562160727926862970580863751454627545335807046743977681218196177274422806391316638988434037714811807205763370063156169170760200000}{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}.

$$x=\frac{166555108488503064587609001029332426562160727926862970580863751454627545335807046743977681218196177274422806391316638988434037714811807205763370063156169170760200000}{49328721959204449568147046034479088694971531566497285433768070211900683062486081977697569624287158160794920423273222183376207903385866241792186913471950016614001}$$