Solve 3x^2-4x/2y=1

$$\frac { 3 x ^ { 2 } - 4 x } { 2 y } = 1$$

Solve for y

$$y=\frac{x\left(3x-4\right)}{2}$$

$$x\neq \frac{4}{3}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2y.

$$3x^{2}-4x=2y$$

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

$$2y=3x^{2}-4x$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{x\left(3x-4\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{x\left(3x-4\right)}{2}$$

Variable y cannot be equal to 0.

$$y=\frac{x\left(3x-4\right)}{2}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{6y+4}+2}{3}$$

$$x=\frac{-\sqrt{6y+4}+2}{3}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{6y+4}+2}{3}$$

$$x=\frac{-\sqrt{6y+4}+2}{3}\text{, }y\geq -\frac{2}{3}\text{ and }y\neq 0$$