Solve 12x^2-18=0

$$12 x ^ { 2 } - 18 = 0$$

Solve for x

$$x = \frac{\sqrt{6}}{2} \approx 1.224744871$$

$$x = -\frac{\sqrt{6}}{2} \approx -1.224744871$$

Steps by Finding Square Root

Add 18 to both sides. Anything plus zero gives itself.

$$12x^{2}=18$$

Divide both sides by 12.

$$x^{2}=\frac{18}{12}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

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

Take the square root of both sides of the equation.

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

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.

$$12x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-18\right)}}{2\times 12}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12\left(-18\right)}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{0±\sqrt{-48\left(-18\right)}}{2\times 12}$$

Multiply -48 times -18.

$$x=\frac{0±\sqrt{864}}{2\times 12}$$

Take the square root of 864.

$$x=\frac{0±12\sqrt{6}}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±12\sqrt{6}}{24}$$

Now solve the equation x=\frac{0±12\sqrt{6}}{24} when ± is plus.

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

Now solve the equation x=\frac{0±12\sqrt{6}}{24} when ± is minus.

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

The equation is now solved.

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