Solve 20-15x^2=0

$$20-15 { x }^{ 2 } =0$$

Solve for x

$$x = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$x = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Steps by Finding Square Root

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-15x^{2}=-20$$

Divide both sides by -15.

$$x^{2}=\frac{-20}{-15}$$

Reduce the fraction \frac{-20}{-15} to lowest terms by extracting and canceling out -5.

$$x^{2}=\frac{4}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{3}}{3} x=-\frac{2\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-15x^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 20}}{2\left(-15\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 20}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60\times 20}}{2\left(-15\right)}$$

Multiply 60 times 20.

$$x=\frac{0±\sqrt{1200}}{2\left(-15\right)}$$

Take the square root of 1200.

$$x=\frac{0±20\sqrt{3}}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{0±20\sqrt{3}}{-30}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{-30} when ± is plus.

$$x=-\frac{2\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{-30} when ± is minus.

$$x=\frac{2\sqrt{3}}{3}$$

The equation is now solved.

$$x=-\frac{2\sqrt{3}}{3} x=\frac{2\sqrt{3}}{3}$$