Solve 2x-4x^2=42*8x2

$$2x-4 { x }^{ 2 } = 42 \cdot 8x2$$

Solve for x_2

$$x_{2}=\frac{x\left(1-2x\right)}{168}$$

Steps for Solving Linear Equation

Multiply 42 and 8 to get 336.

$$2x-4x^{2}=336x_{2}$$

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

$$336x_{2}=2x-4x^{2}$$

Divide both sides by 336.

$$\frac{336x_{2}}{336}=\frac{2x\left(1-2x\right)}{336}$$

Dividing by 336 undoes the multiplication by 336.

$$x_{2}=\frac{2x\left(1-2x\right)}{336}$$

Divide 2x\left(1-2x\right) by 336.

$$x_{2}=\frac{x\left(1-2x\right)}{168}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{1-1344x_{2}}+1}{4}$$

$$x=\frac{\sqrt{1-1344x_{2}}+1}{4}$$

Solve for x

$$x=\frac{-\sqrt{1-1344x_{2}}+1}{4}$$

$$x=\frac{\sqrt{1-1344x_{2}}+1}{4}\text{, }x_{2}\leq \frac{1}{1344}$$