Solve 4x^2+5y+6z=10

$$4 x ^ { 2 } + 5 y + 6 z = 10$$

Solve for y

$$y=-\frac{4x^{2}}{5}-\frac{6z}{5}+2$$

Steps for Solving Linear Equation

Subtract 4x^{2} from both sides.

$$5y+6z=10-4x^{2}$$

Subtract 6z from both sides.

$$5y=10-4x^{2}-6z$$

The equation is in standard form.

$$5y=10-6z-4x^{2}$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{10-6z-4x^{2}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{10-6z-4x^{2}}{5}$$

Divide 10-4x^{2}-6z by 5.

$$y=-\frac{4x^{2}}{5}-\frac{6z}{5}+2$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{10-6z-5y}}{2}$$

$$x=\frac{\sqrt{10-6z-5y}}{2}$$

Solve for x

$$x=\frac{\sqrt{10-6z-5y}}{2}$$

$$x=-\frac{\sqrt{10-6z-5y}}{2}\text{, }y\leq -\frac{6z}{5}+2$$