Solve 3x^2+6x7=x

$$3 { x }^{ 2 } +6x7=x$$

Solve for x_7

$$x_{7}=-\frac{x\left(3x-1\right)}{6}$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides.

$$6x_{7}=x-3x^{2}$$

Divide both sides by 6.

$$\frac{6x_{7}}{6}=\frac{x\left(1-3x\right)}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x_{7}=\frac{x\left(1-3x\right)}{6}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{1-72x_{7}}+1}{6}$$

$$x=\frac{-\sqrt{1-72x_{7}}+1}{6}$$

Solve for x

$$x=\frac{\sqrt{1-72x_{7}}+1}{6}$$

$$x=\frac{-\sqrt{1-72x_{7}}+1}{6}\text{, }x_{7}\leq \frac{1}{72}$$