Solve -3x^2+21=13

$$- 3 x ^ { 2 } + 21 = 13$$

Solve for x

$$x = \frac{2 \sqrt{6}}{3} \approx 1.632993162$$

$$x = -\frac{2 \sqrt{6}}{3} \approx -1.632993162$$

Steps by Finding Square Root

Subtract 21 from both sides.

$$-3x^{2}=13-21$$

Subtract 21 from 13 to get -8.

$$-3x^{2}=-8$$

Divide both sides by -3.

$$x^{2}=\frac{-8}{-3}$$

Fraction \frac{-8}{-3} can be simplified to \frac{8}{3} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{8}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{6}}{3} x=-\frac{2\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract 13 from both sides.

$$-3x^{2}+21-13=0$$

Subtract 13 from 21 to get 8.

$$-3x^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 8}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 8}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 8}}{2\left(-3\right)}$$

Multiply 12 times 8.

$$x=\frac{0±\sqrt{96}}{2\left(-3\right)}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±4\sqrt{6}}{-6}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{-6} when ± is plus.

$$x=-\frac{2\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{-6} when ± is minus.

$$x=\frac{2\sqrt{6}}{3}$$

The equation is now solved.

$$x=-\frac{2\sqrt{6}}{3} x=\frac{2\sqrt{6}}{3}$$