Solve 5/2t^2=12

$$\frac { 5 } { 2 } t ^ { 2 } = 12$$

Solve for t

$$t = \frac{2 \sqrt{30}}{5} \approx 2.19089023$$

$$t = -\frac{2 \sqrt{30}}{5} \approx -2.19089023$$

Steps by Finding Square Root

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$t^{2}=12\times \frac{2}{5}$$

Multiply 12 and \frac{2}{5} to get \frac{24}{5}.

$$t^{2}=\frac{24}{5}$$

Take the square root of both sides of the equation.

$$t=\frac{2\sqrt{30}}{5} t=-\frac{2\sqrt{30}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$t^{2}=12\times \frac{2}{5}$$

Multiply 12 and \frac{2}{5} to get \frac{24}{5}.

$$t^{2}=\frac{24}{5}$$

Subtract \frac{24}{5} from both sides.

$$t^{2}-\frac{24}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{24}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{24}{5}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{24}{5}\right)}}{2}$$

Multiply -4 times -\frac{24}{5}.

$$t=\frac{0±\sqrt{\frac{96}{5}}}{2}$$

Take the square root of \frac{96}{5}.

$$t=\frac{0±\frac{4\sqrt{30}}{5}}{2}$$

Now solve the equation t=\frac{0±\frac{4\sqrt{30}}{5}}{2} when ± is plus.

$$t=\frac{2\sqrt{30}}{5}$$

Now solve the equation t=\frac{0±\frac{4\sqrt{30}}{5}}{2} when ± is minus.

$$t=-\frac{2\sqrt{30}}{5}$$

The equation is now solved.

$$t=\frac{2\sqrt{30}}{5} t=-\frac{2\sqrt{30}}{5}$$