Solve 36/4x-2+8x=12y-3/5

$$\frac { 36 } { 4 x - 2 } + 8 x = \frac { 12 y - 3 } { 5 }$$

Solve for y

$$y=-\frac{80x^{2}-34x+87}{12\left(1-2x\right)}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10\left(2x-1\right), the least common multiple of 4x-2,5.

$$5\times 36+8x\times 10\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

Multiply 5 and 36 to get 180.

$$180+8x\times 10\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

Multiply 8 and 10 to get 80.

$$180+80x\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

Use the distributive property to multiply 80x by 2x-1.

$$180+160x^{2}-80x=\left(4x-2\right)\left(12y-3\right)$$

Use the distributive property to multiply 4x-2 by 12y-3.

$$180+160x^{2}-80x=48xy-12x-24y+6$$

Swap sides so that all variable terms are on the left hand side.

$$48xy-12x-24y+6=180+160x^{2}-80x$$

Add 12x to both sides.

$$48xy-24y+6=180+160x^{2}-80x+12x$$

Combine -80x and 12x to get -68x.

$$48xy-24y+6=180+160x^{2}-68x$$

Subtract 6 from both sides.

$$48xy-24y=180+160x^{2}-68x-6$$

Subtract 6 from 180 to get 174.

$$48xy-24y=174+160x^{2}-68x$$

Combine all terms containing y.

$$\left(48x-24\right)y=174+160x^{2}-68x$$

The equation is in standard form.

$$\left(48x-24\right)y=160x^{2}-68x+174$$

Divide both sides by 48x-24.

$$\frac{\left(48x-24\right)y}{48x-24}=\frac{160x^{2}-68x+174}{48x-24}$$

Dividing by 48x-24 undoes the multiplication by 48x-24.

$$y=\frac{160x^{2}-68x+174}{48x-24}$$

Divide 174+160x^{2}-68x by 48x-24.

$$y=\frac{80x^{2}-34x+87}{12\left(2x-1\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

$$x=-\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

Solve for x

$$x=\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

$$x=-\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}\text{, }y\geq 5\sqrt{2}+\frac{23}{12}\text{ or }y\leq \frac{23}{12}-5\sqrt{2}$$