Solve 3x^2+mx+10=0

$$3 x ^ { 2 } + m x + 10 = 0$$

Solve for m

$$m=-3x-\frac{10}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$mx+10=-3x^{2}$$

Subtract 10 from both sides.

$$mx=-3x^{2}-10$$

The equation is in standard form.

$$xm=-3x^{2}-10$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{-3x^{2}-10}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{-3x^{2}-10}{x}$$

Divide -3x^{2}-10 by x.

$$m=-3x-\frac{10}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{m^{2}-120}-m}{6}$$

$$x=\frac{-\sqrt{m^{2}-120}-m}{6}$$

Solve for x

$$x=\frac{\sqrt{m^{2}-120}-m}{6}$$

$$x=\frac{-\sqrt{m^{2}-120}-m}{6}\text{, }|m|\geq 2\sqrt{30}$$