Solve 3x^2+20=96

$$3 { x }^{ 2 } +20=96$$

Solve for x

$$x = \frac{2 \sqrt{57}}{3} \approx 5.033222957$$

$$x = -\frac{2 \sqrt{57}}{3} \approx -5.033222957$$

Steps by Finding Square Root

Subtract 20 from both sides.

$$3x^{2}=96-20$$

Subtract 20 from 96 to get 76.

$$3x^{2}=76$$

Divide both sides by 3.

$$x^{2}=\frac{76}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{57}}{3} x=-\frac{2\sqrt{57}}{3}$$

Steps Using the Quadratic Formula

Subtract 96 from both sides.

$$3x^{2}+20-96=0$$

Subtract 96 from 20 to get -76.

$$3x^{2}-76=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -76 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-76\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-76\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-76\right)}}{2\times 3}$$

Multiply -12 times -76.

$$x=\frac{0±\sqrt{912}}{2\times 3}$$

Take the square root of 912.

$$x=\frac{0±4\sqrt{57}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±4\sqrt{57}}{6}$$

Now solve the equation x=\frac{0±4\sqrt{57}}{6} when ± is plus.

$$x=\frac{2\sqrt{57}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{57}}{6} when ± is minus.

$$x=-\frac{2\sqrt{57}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{57}}{3} x=-\frac{2\sqrt{57}}{3}$$