Solve x(x-1)/2=4x7

$$\frac { x ( x - 1 ) } { 2 } = 4 x 7$$

Solve for x_7

$$x_{7}=\frac{x\left(x-1\right)}{8}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$x\left(x-1\right)=8x_{7}$$

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

$$x^{2}-x=8x_{7}$$

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

$$8x_{7}=x^{2}-x$$

Divide both sides by 8.

$$\frac{8x_{7}}{8}=\frac{x\left(x-1\right)}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x_{7}=\frac{x\left(x-1\right)}{8}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{32x_{7}+1}+1}{2}$$

$$x=\frac{-\sqrt{32x_{7}+1}+1}{2}$$

Solve for x

$$x=\frac{\sqrt{32x_{7}+1}+1}{2}$$

$$x=\frac{-\sqrt{32x_{7}+1}+1}{2}\text{, }x_{7}\geq -\frac{1}{32}$$