Solve 21-3x^2=0

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

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

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

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

Divide both sides by -3.

$$x^{2}=\frac{-21}{-3}$$

Divide -21 by -3 to get 7.

$$x^{2}=7$$

Take the square root of both sides of the equation.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 21}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 21}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 21}}{2\left(-3\right)}$$

Multiply 12 times 21.

$$x=\frac{0±\sqrt{252}}{2\left(-3\right)}$$

Take the square root of 252.

$$x=\frac{0±6\sqrt{7}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±6\sqrt{7}}{-6}$$

Now solve the equation x=\frac{0±6\sqrt{7}}{-6} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{7}}{-6} when ± is minus.

$$x=\sqrt{7}$$

The equation is now solved.

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