Solve 3x^2-2=8

$$3 x ^ { 2 } - 2 = 8$$

Solve for x

$$x = \frac{\sqrt{30}}{3} \approx 1.825741858$$

$$x = -\frac{\sqrt{30}}{3} \approx -1.825741858$$

Steps by Finding Square Root

Add 2 to both sides.

$$3x^{2}=8+2$$

Add 8 and 2 to get 10.

$$3x^{2}=10$$

Divide both sides by 3.

$$x^{2}=\frac{10}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{3} x=-\frac{\sqrt{30}}{3}$$

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$3x^{2}-2-8=0$$

Subtract 8 from -2 to get -10.

$$3x^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-10\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-10\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-10\right)}}{2\times 3}$$

Multiply -12 times -10.

$$x=\frac{0±\sqrt{120}}{2\times 3}$$

Take the square root of 120.

$$x=\frac{0±2\sqrt{30}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{30}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{6} when ± is plus.

$$x=\frac{\sqrt{30}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{6} when ± is minus.

$$x=-\frac{\sqrt{30}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{3} x=-\frac{\sqrt{30}}{3}$$