Solve 3/4v^2=61

$$\frac { 3 } { 4 } v ^ { 2 } = 61$$

Solve for v

$$v = \frac{2 \sqrt{183}}{3} \approx 9.018499506$$

$$v = -\frac{2 \sqrt{183}}{3} \approx -9.018499506$$

Steps by Finding Square Root

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$v^{2}=61\times \frac{4}{3}$$

Multiply 61 and \frac{4}{3} to get \frac{244}{3}.

$$v^{2}=\frac{244}{3}$$

Take the square root of both sides of the equation.

$$v=\frac{2\sqrt{183}}{3} v=-\frac{2\sqrt{183}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$v^{2}=61\times \frac{4}{3}$$

Multiply 61 and \frac{4}{3} to get \frac{244}{3}.

$$v^{2}=\frac{244}{3}$$

Subtract \frac{244}{3} from both sides.

$$v^{2}-\frac{244}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{244}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-\frac{244}{3}\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-\frac{244}{3}\right)}}{2}$$

Multiply -4 times -\frac{244}{3}.

$$v=\frac{0±\sqrt{\frac{976}{3}}}{2}$$

Take the square root of \frac{976}{3}.

$$v=\frac{0±\frac{4\sqrt{183}}{3}}{2}$$

Now solve the equation v=\frac{0±\frac{4\sqrt{183}}{3}}{2} when ± is plus.

$$v=\frac{2\sqrt{183}}{3}$$

Now solve the equation v=\frac{0±\frac{4\sqrt{183}}{3}}{2} when ± is minus.

$$v=-\frac{2\sqrt{183}}{3}$$

The equation is now solved.

$$v=\frac{2\sqrt{183}}{3} v=-\frac{2\sqrt{183}}{3}$$