Solve 12x^2-5-2=0

$$12 x ^ { 2 } - 5 - 2 = 0$$

Solve for x

$$x=\frac{\sqrt{21}}{6}\approx 0.763762616$$

$$x=-\frac{\sqrt{21}}{6}\approx -0.763762616$$

Steps by Finding Square Root

Subtract 2 from -5 to get -7.

$$12x^{2}-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$12x^{2}=7$$

Divide both sides by 12.

$$x^{2}=\frac{7}{12}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{21}}{6} x=-\frac{\sqrt{21}}{6}$$

Steps Using the Quadratic Formula

Subtract 2 from -5 to get -7.

$$12x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-7\right)}}{2\times 12}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12\left(-7\right)}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{0±\sqrt{-48\left(-7\right)}}{2\times 12}$$

Multiply -48 times -7.

$$x=\frac{0±\sqrt{336}}{2\times 12}$$

Take the square root of 336.

$$x=\frac{0±4\sqrt{21}}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±4\sqrt{21}}{24}$$

Now solve the equation x=\frac{0±4\sqrt{21}}{24} when ± is plus.

$$x=\frac{\sqrt{21}}{6}$$

Now solve the equation x=\frac{0±4\sqrt{21}}{24} when ± is minus.

$$x=-\frac{\sqrt{21}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{21}}{6} x=-\frac{\sqrt{21}}{6}$$