Solve 4x^2-5xy-14=0

$$4 { x }^{ 2 } -5xy-14=0$$

Solve for y

$$y=\frac{4x}{5}-\frac{14}{5x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 4x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-5xy-14=-4x^{2}$$

Add 14 to both sides.

$$-5xy=-4x^{2}+14$$

The equation is in standard form.

$$\left(-5x\right)y=14-4x^{2}$$

Divide both sides by -5x.

$$\frac{\left(-5x\right)y}{-5x}=\frac{14-4x^{2}}{-5x}$$

Dividing by -5x undoes the multiplication by -5x.

$$y=\frac{14-4x^{2}}{-5x}$$

Divide -4x^{2}+14 by -5x.

$$y=\frac{4x}{5}-\frac{14}{5x}$$

Solve for x

$$x=\frac{\sqrt{25y^{2}+224}+5y}{8}$$

$$x=\frac{-\sqrt{25y^{2}+224}+5y}{8}$$