Solve 24x^2/2=8

$$\frac{ 24 { x }^{ 2 } }{ 2 } =8$$

Solve for x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Multiply both sides by 2.

$$24x^{2}=8\times 2$$

Multiply 8 and 2 to get 16.

$$24x^{2}=16$$

Divide both sides by 24.

$$x^{2}=\frac{16}{24}$$

Reduce the fraction \frac{16}{24} to lowest terms by extracting and canceling out 8.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$24x^{2}=8\times 2$$

Multiply 8 and 2 to get 16.

$$24x^{2}=16$$

Subtract 16 from both sides.

$$24x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 24 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 24\left(-16\right)}}{2\times 24}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 24\left(-16\right)}}{2\times 24}$$

Multiply -4 times 24.

$$x=\frac{0±\sqrt{-96\left(-16\right)}}{2\times 24}$$

Multiply -96 times -16.

$$x=\frac{0±\sqrt{1536}}{2\times 24}$$

Take the square root of 1536.

$$x=\frac{0±16\sqrt{6}}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{0±16\sqrt{6}}{48}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{48} when ± is plus.

$$x=\frac{\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{48} when ± is minus.

$$x=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$