Solve 4x^2+6=12

$$4 x ^ { 2 } + 6 = 12$$

Solve for x

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

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

Steps by Finding Square Root

Subtract 6 from both sides.

$$4x^{2}=12-6$$

Subtract 6 from 12 to get 6.

$$4x^{2}=6$$

Divide both sides by 4.

$$x^{2}=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

Subtract 12 from both sides.

$$4x^{2}+6-12=0$$

Subtract 12 from 6 to get -6.

$$4x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-6\right)}}{2\times 4}$$

Multiply -16 times -6.

$$x=\frac{0±\sqrt{96}}{2\times 4}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{6}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{8} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{6}}{8} when ± is minus.

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

The equation is now solved.

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