Solve 9.2=80*v^2/0.6

$$9.2 = 80 \times \frac { v ^ { 2 } } { 0.6 }$$

Solve for v

$$v=\frac{\sqrt{690}}{100}\approx 0.262678511$$

$$v=-\frac{\sqrt{690}}{100}\approx -0.262678511$$

Steps by Finding Square Root

Divide both sides by 80.

$$\frac{9.2}{80}=\frac{v^{2}}{0.6}$$

Expand \frac{9.2}{80} by multiplying both numerator and the denominator by 10.

$$\frac{92}{800}=\frac{v^{2}}{0.6}$$

Reduce the fraction \frac{92}{800} to lowest terms by extracting and canceling out 4.

$$\frac{23}{200}=\frac{v^{2}}{0.6}$$

Multiply both sides by 0.6.

$$\frac{23}{200}\times 0.6=v^{2}$$

Multiply \frac{23}{200} and 0.6 to get \frac{69}{1000}.

$$\frac{69}{1000}=v^{2}$$

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

$$v^{2}=\frac{69}{1000}$$

Take the square root of both sides of the equation.

$$v=\frac{\sqrt{690}}{100} v=-\frac{\sqrt{690}}{100}$$

Steps Using the Quadratic Formula

Divide both sides by 80.

$$\frac{9.2}{80}=\frac{v^{2}}{0.6}$$

Expand \frac{9.2}{80} by multiplying both numerator and the denominator by 10.

$$\frac{92}{800}=\frac{v^{2}}{0.6}$$

Reduce the fraction \frac{92}{800} to lowest terms by extracting and canceling out 4.

$$\frac{23}{200}=\frac{v^{2}}{0.6}$$

Multiply both sides by 0.6.

$$\frac{23}{200}\times 0.6=v^{2}$$

Multiply \frac{23}{200} and 0.6 to get \frac{69}{1000}.

$$\frac{69}{1000}=v^{2}$$

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

$$v^{2}=\frac{69}{1000}$$

Subtract \frac{69}{1000} from both sides.

$$v^{2}-\frac{69}{1000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{69}{1000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-\frac{69}{1000}\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-\frac{69}{1000}\right)}}{2}$$

Multiply -4 times -\frac{69}{1000}.

$$v=\frac{0±\sqrt{\frac{69}{250}}}{2}$$

Take the square root of \frac{69}{250}.

$$v=\frac{0±\frac{\sqrt{690}}{50}}{2}$$

Now solve the equation v=\frac{0±\frac{\sqrt{690}}{50}}{2} when ± is plus.

$$v=\frac{\sqrt{690}}{100}$$

Now solve the equation v=\frac{0±\frac{\sqrt{690}}{50}}{2} when ± is minus.

$$v=-\frac{\sqrt{690}}{100}$$

The equation is now solved.

$$v=\frac{\sqrt{690}}{100} v=-\frac{\sqrt{690}}{100}$$