Solve 3x^2+20x_{0}-100=0

$$3 x ^ { 2 } + 20 x _ { 0 } - 100 = 0$$

Solve for x_0

$$x_{0}=-\frac{3x^{2}}{20}+5$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$20x_{0}-100=-3x^{2}$$

Add 100 to both sides.

$$20x_{0}=-3x^{2}+100$$

The equation is in standard form.

$$20x_{0}=100-3x^{2}$$

Divide both sides by 20.

$$\frac{20x_{0}}{20}=\frac{100-3x^{2}}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$x_{0}=\frac{100-3x^{2}}{20}$$

Divide -3x^{2}+100 by 20.

$$x_{0}=-\frac{3x^{2}}{20}+5$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{75-15x_{0}}}{3}$$

$$x=\frac{2\sqrt{75-15x_{0}}}{3}$$

Solve for x

$$x=\frac{2\sqrt{75-15x_{0}}}{3}$$

$$x=-\frac{2\sqrt{75-15x_{0}}}{3}\text{, }x_{0}\leq 5$$