Solve 7.5=5t^2

$$7.5 = 5 t ^ { 2 }$$

Solve for t

$$t = \frac{\sqrt{6}}{2} \approx 1.224744871$$

$$t = -\frac{\sqrt{6}}{2} \approx -1.224744871$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{7.5}{5}=t^{2}$$

Expand \frac{7.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{75}{50}=t^{2}$$

Reduce the fraction \frac{75}{50} to lowest terms by extracting and canceling out 25.

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

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

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

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{6}}{2} t=-\frac{\sqrt{6}}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$\frac{7.5}{5}=t^{2}$$

Expand \frac{7.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{75}{50}=t^{2}$$

Reduce the fraction \frac{75}{50} to lowest terms by extracting and canceling out 25.

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

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

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

Subtract \frac{3}{2} from both sides.

$$t^{2}-\frac{3}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{2}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{3}{2}\right)}}{2}$$

Multiply -4 times -\frac{3}{2}.

$$t=\frac{0±\sqrt{6}}{2}$$

Now solve the equation t=\frac{0±\sqrt{6}}{2} when ± is plus.

$$t=\frac{\sqrt{6}}{2}$$

Now solve the equation t=\frac{0±\sqrt{6}}{2} when ± is minus.

$$t=-\frac{\sqrt{6}}{2}$$

The equation is now solved.

$$t=\frac{\sqrt{6}}{2} t=-\frac{\sqrt{6}}{2}$$