Solve 2=15x^2-24

$$2 = 15 x ^ { 2 } - 24$$

Solve for x

$$x = \frac{\sqrt{390}}{15} \approx 1.316561177$$

$$x = -\frac{\sqrt{390}}{15} \approx -1.316561177$$

Steps by Finding Square Root

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

$$15x^{2}-24=2$$

Add 24 to both sides.

$$15x^{2}=2+24$$

Add 2 and 24 to get 26.

$$15x^{2}=26$$

Divide both sides by 15.

$$x^{2}=\frac{26}{15}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{390}}{15} x=-\frac{\sqrt{390}}{15}$$

Steps Using the Quadratic Formula

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

$$15x^{2}-24=2$$

Subtract 2 from both sides.

$$15x^{2}-24-2=0$$

Subtract 2 from -24 to get -26.

$$15x^{2}-26=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 15 for a, 0 for b, and -26 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 15\left(-26\right)}}{2\times 15}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 15\left(-26\right)}}{2\times 15}$$

Multiply -4 times 15.

$$x=\frac{0±\sqrt{-60\left(-26\right)}}{2\times 15}$$

Multiply -60 times -26.

$$x=\frac{0±\sqrt{1560}}{2\times 15}$$

Take the square root of 1560.

$$x=\frac{0±2\sqrt{390}}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{0±2\sqrt{390}}{30}$$

Now solve the equation x=\frac{0±2\sqrt{390}}{30} when ± is plus.

$$x=\frac{\sqrt{390}}{15}$$

Now solve the equation x=\frac{0±2\sqrt{390}}{30} when ± is minus.

$$x=-\frac{\sqrt{390}}{15}$$

The equation is now solved.

$$x=\frac{\sqrt{390}}{15} x=-\frac{\sqrt{390}}{15}$$