Solve 24x^2-8=98

$$24 { x }^{ 2 } -8 = 98$$

Solve for x

$$x = \frac{\sqrt{159}}{6} \approx 2.101586702$$

$$x = -\frac{\sqrt{159}}{6} \approx -2.101586702$$

Steps by Finding Square Root

Add 8 to both sides.

$$24x^{2}=98+8$$

Add 98 and 8 to get 106.

$$24x^{2}=106$$

Divide both sides by 24.

$$x^{2}=\frac{106}{24}$$

Reduce the fraction \frac{106}{24} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{53}{12}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{159}}{6} x=-\frac{\sqrt{159}}{6}$$

Steps Using the Quadratic Formula

Subtract 98 from both sides.

$$24x^{2}-8-98=0$$

Subtract 98 from -8 to get -106.

$$24x^{2}-106=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 24 for a, 0 for b, and -106 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 24\left(-106\right)}}{2\times 24}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 24\left(-106\right)}}{2\times 24}$$

Multiply -4 times 24.

$$x=\frac{0±\sqrt{-96\left(-106\right)}}{2\times 24}$$

Multiply -96 times -106.

$$x=\frac{0±\sqrt{10176}}{2\times 24}$$

Take the square root of 10176.

$$x=\frac{0±8\sqrt{159}}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{0±8\sqrt{159}}{48}$$

Now solve the equation x=\frac{0±8\sqrt{159}}{48} when ± is plus.

$$x=\frac{\sqrt{159}}{6}$$

Now solve the equation x=\frac{0±8\sqrt{159}}{48} when ± is minus.

$$x=-\frac{\sqrt{159}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{159}}{6} x=-\frac{\sqrt{159}}{6}$$