Solve 5x^2-6x_{0}-18=0

$$5 x ^ { 2 } - 6 x _ { 0 } - 18 = 0$$

Solve for x_0

$$x_{0}=\frac{5x^{2}}{6}-3$$

Steps for Solving Linear Equation

Subtract 5x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-6x_{0}-18=-5x^{2}$$

Add 18 to both sides.

$$-6x_{0}=-5x^{2}+18$$

The equation is in standard form.

$$-6x_{0}=18-5x^{2}$$

Divide both sides by -6.

$$\frac{-6x_{0}}{-6}=\frac{18-5x^{2}}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$x_{0}=\frac{18-5x^{2}}{-6}$$

Divide -5x^{2}+18 by -6.

$$x_{0}=\frac{5x^{2}}{6}-3$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{30\left(x_{0}+3\right)}}{5}$$

$$x=\frac{\sqrt{30\left(x_{0}+3\right)}}{5}$$

Solve for x

$$x=\frac{\sqrt{30\left(x_{0}+3\right)}}{5}$$

$$x=-\frac{\sqrt{30\left(x_{0}+3\right)}}{5}\text{, }x_{0}\geq -3$$