Solve 3x^2-8=7

$$3 x ^ { 2 } - 8 = 7$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Add 8 to both sides.

$$3x^{2}=7+8$$

Add 7 and 8 to get 15.

$$3x^{2}=15$$

Divide both sides by 3.

$$x^{2}=\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

$$x=\sqrt{5} x=-\sqrt{5}$$

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$3x^{2}-8-7=0$$

Subtract 7 from -8 to get -15.

$$3x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-15\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-15\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-15\right)}}{2\times 3}$$

Multiply -12 times -15.

$$x=\frac{0±\sqrt{180}}{2\times 3}$$

Take the square root of 180.

$$x=\frac{0±6\sqrt{5}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{5}}{6}$$

Now solve the equation x=\frac{0±6\sqrt{5}}{6} when ± is plus.

$$x=\sqrt{5}$$

Now solve the equation x=\frac{0±6\sqrt{5}}{6} when ± is minus.

$$x=-\sqrt{5}$$

The equation is now solved.

$$x=\sqrt{5} x=-\sqrt{5}$$