Solve 4x^2y-3x^2=25

$$4 x ^ { 2 } y - 3 x ^ { 2 } = 25$$

Solve for y

$$y=\frac{3}{4}+\frac{25}{4x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add 3x^{2} to both sides.

$$4x^{2}y=25+3x^{2}$$

The equation is in standard form.

$$4x^{2}y=3x^{2}+25$$

Divide both sides by 4x^{2}.

$$\frac{4x^{2}y}{4x^{2}}=\frac{3x^{2}+25}{4x^{2}}$$

Dividing by 4x^{2} undoes the multiplication by 4x^{2}.

$$y=\frac{3x^{2}+25}{4x^{2}}$$

Divide 25+3x^{2} by 4x^{2}.

$$y=\frac{3}{4}+\frac{25}{4x^{2}}$$

Solve for x (complex solution)

$$x=-5\left(4y-3\right)^{-\frac{1}{2}}$$

$$x=5\left(4y-3\right)^{-\frac{1}{2}}\text{, }y\neq \frac{3}{4}$$

Solve for x

$$x=\frac{5}{\sqrt{4y-3}}$$

$$x=-\frac{5}{\sqrt{4y-3}}\text{, }y>\frac{3}{4}$$