Solve -12x^2+21=0

$$- 12 x ^ { 2 } + 21 = 0$$

Solve for x

$$x = \frac{\sqrt{7}}{2} \approx 1.322875656$$

$$x = -\frac{\sqrt{7}}{2} \approx -1.322875656$$

Steps by Finding Square Root

Subtract 21 from both sides. Anything subtracted from zero gives its negation.

$$-12x^{2}=-21$$

Divide both sides by -12.

$$x^{2}=\frac{-21}{-12}$$

Reduce the fraction \frac{-21}{-12} to lowest terms by extracting and canceling out -3.

$$x^{2}=\frac{7}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{7}}{2} x=-\frac{\sqrt{7}}{2}$$

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.

$$-12x^{2}+21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -12 for a, 0 for b, and 21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 21}}{2\left(-12\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 21}}{2\left(-12\right)}$$

Multiply -4 times -12.

$$x=\frac{0±\sqrt{48\times 21}}{2\left(-12\right)}$$

Multiply 48 times 21.

$$x=\frac{0±\sqrt{1008}}{2\left(-12\right)}$$

Take the square root of 1008.

$$x=\frac{0±12\sqrt{7}}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{0±12\sqrt{7}}{-24}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{-24} when ± is plus.

$$x=-\frac{\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{-24} when ± is minus.

$$x=\frac{\sqrt{7}}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{7}}{2} x=\frac{\sqrt{7}}{2}$$