Solve 4x^2=(3(x-2)-5(2y)/4)

$$4 x ^ { 2 } = ( \frac { 3 ( x - 2 ) - 5 ( 2 y ) } { 4 } )$$

Solve for y

$$y=-\frac{8x^{2}}{5}+\frac{3x}{10}-\frac{3}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$16x^{2}=3\left(x-2\right)-5\times 2y$$

Use the distributive property to multiply 3 by x-2.

$$16x^{2}=3x-6-5\times 2y$$

Multiply 5 and 2 to get 10.

$$16x^{2}=3x-6-10y$$

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

$$3x-6-10y=16x^{2}$$

Subtract 3x from both sides.

$$-6-10y=16x^{2}-3x$$

Add 6 to both sides.

$$-10y=16x^{2}-3x+6$$

Divide both sides by -10.

$$\frac{-10y}{-10}=\frac{16x^{2}-3x+6}{-10}$$

Dividing by -10 undoes the multiplication by -10.

$$y=\frac{16x^{2}-3x+6}{-10}$$

Divide 16x^{2}-3x+6 by -10.

$$y=-\frac{8x^{2}}{5}+\frac{3x}{10}-\frac{3}{5}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{-640y-375}+3}{32}$$

$$x=\frac{-\sqrt{-640y-375}+3}{32}$$

Solve for x

$$x=\frac{\sqrt{-640y-375}+3}{32}$$

$$x=\frac{-\sqrt{-640y-375}+3}{32}\text{, }y\leq -\frac{75}{128}$$