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

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

Solvi għal y

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

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'10\left(2x-1\right), l-inqas denominatur komuni ta' 4x-2,5.

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

Immultiplika 5 u 36 biex tikseb 180.

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

Immultiplika 8 u 10 biex tikseb 80.

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

Uża l-propjetà distributtiva biex timmultiplika 80x b'2x-1.

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

Uża l-propjetà distributtiva biex timmultiplika 4x-2 b'12y-3.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Żid 12x maż-żewġ naħat.

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

Ikkombina -80x u 12x biex tikseb -68x.

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

Naqqas 6 miż-żewġ naħat.

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

Naqqas 6 minn 180 biex tikseb 174.

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

Ikkombina t-termini kollha li fihom y.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'48x-24.

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

Meta tiddividi b'48x-24 titneħħa l-multiplikazzjoni b'48x-24.

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

Iddividi 174+160x^{2}-68x b'48x-24.

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

Solvi għal x (complex solution)

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

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

Solvi għal x

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

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