$\fraction{4 x + 6}{12 x + 4} = \fraction{2 x}{6}$

## 共享

3\left(4x+6\right)=\left(6x+2\right)\times 2x

12x+18=\left(6x+2\right)\times 2x

12x+18=\left(12x+4\right)x

12x+18=12x^{2}+4x

12x+18-12x^{2}=4x

12x+18-12x^{2}-4x=0

8x+18-12x^{2}=0

-12x^{2}+8x+18=0

x=\frac{-8±\sqrt{8^{2}-4\left(-12\right)\times 18}}{2\left(-12\right)}

x=\frac{-8±\sqrt{64-4\left(-12\right)\times 18}}{2\left(-12\right)}

x=\frac{-8±\sqrt{64+48\times 18}}{2\left(-12\right)}

x=\frac{-8±\sqrt{64+864}}{2\left(-12\right)}

x=\frac{-8±\sqrt{928}}{2\left(-12\right)}

x=\frac{-8±4\sqrt{58}}{2\left(-12\right)}

x=\frac{-8±4\sqrt{58}}{-24}

x=\frac{4\sqrt{58}-8}{-24}

x=-\frac{\sqrt{58}}{6}+\frac{1}{3}
-8+4\sqrt{58} 除以 -24。
x=\frac{-4\sqrt{58}-8}{-24}

x=\frac{\sqrt{58}}{6}+\frac{1}{3}
-8-4\sqrt{58} 除以 -24。
x=-\frac{\sqrt{58}}{6}+\frac{1}{3} x=\frac{\sqrt{58}}{6}+\frac{1}{3}

3\left(4x+6\right)=\left(6x+2\right)\times 2x

12x+18=\left(6x+2\right)\times 2x

12x+18=\left(12x+4\right)x

12x+18=12x^{2}+4x

12x+18-12x^{2}=4x

12x+18-12x^{2}-4x=0

8x+18-12x^{2}=0

8x-12x^{2}=-18

-12x^{2}+8x=-18

\frac{-12x^{2}+8x}{-12}=-\frac{18}{-12}

x^{2}+\frac{8}{-12}x=-\frac{18}{-12}

x^{2}-\frac{2}{3}x=-\frac{18}{-12}

x^{2}-\frac{2}{3}x=\frac{3}{2}

x^{2}-\frac{2}{3}x+\left(-\frac{1}{3}\right)^{2}=\frac{3}{2}+\left(-\frac{1}{3}\right)^{2}

x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{3}{2}+\frac{1}{9}

x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{29}{18}

\left(x-\frac{1}{3}\right)^{2}=\frac{29}{18}

\sqrt{\left(x-\frac{1}{3}\right)^{2}}=\sqrt{\frac{29}{18}}

x-\frac{1}{3}=\frac{\sqrt{58}}{6} x-\frac{1}{3}=-\frac{\sqrt{58}}{6}

x=\frac{\sqrt{58}}{6}+\frac{1}{3} x=-\frac{\sqrt{58}}{6}+\frac{1}{3}