Solve 90/x^2=24

$$\frac { 90 } { x ^ { 2 } } = 24$$

Solve for x

$$x = \frac{\sqrt{15}}{2} \approx 1.936491673$$

$$x = -\frac{\sqrt{15}}{2} \approx -1.936491673$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$90=24x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$24x^{2}=90$$

Divide both sides by 24.

$$x^{2}=\frac{90}{24}$$

Reduce the fraction \frac{90}{24} to lowest terms by extracting and canceling out 6.

$$x^{2}=\frac{15}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15}}{2} x=-\frac{\sqrt{15}}{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$90=24x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$24x^{2}=90$$

Subtract 90 from both sides.

$$24x^{2}-90=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 24 for a, 0 for b, and -90 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 24\left(-90\right)}}{2\times 24}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 24\left(-90\right)}}{2\times 24}$$

Multiply -4 times 24.

$$x=\frac{0±\sqrt{-96\left(-90\right)}}{2\times 24}$$

Multiply -96 times -90.

$$x=\frac{0±\sqrt{8640}}{2\times 24}$$

Take the square root of 8640.

$$x=\frac{0±24\sqrt{15}}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{0±24\sqrt{15}}{48}$$

Now solve the equation x=\frac{0±24\sqrt{15}}{48} when ± is plus.

$$x=\frac{\sqrt{15}}{2}$$

Now solve the equation x=\frac{0±24\sqrt{15}}{48} when ± is minus.

$$x=-\frac{\sqrt{15}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{15}}{2} x=-\frac{\sqrt{15}}{2}$$