Solve 20=3.86/2t^2

$$20 = \frac { 3.86 } { 2 } t ^ { 2 }$$

Solve for t

$$t = \frac{20 \sqrt{965}}{193} \approx 3.2191139$$

$$t = -\frac{20 \sqrt{965}}{193} \approx -3.2191139$$

Steps by Finding Square Root

Expand \frac{3.86}{2} by multiplying both numerator and the denominator by 100.

$$20=\frac{386}{200}t^{2}$$

Reduce the fraction \frac{386}{200} to lowest terms by extracting and canceling out 2.

$$20=\frac{193}{100}t^{2}$$

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

$$\frac{193}{100}t^{2}=20$$

Multiply both sides by \frac{100}{193}, the reciprocal of \frac{193}{100}.

$$t^{2}=20\times \frac{100}{193}$$

Multiply 20 and \frac{100}{193} to get \frac{2000}{193}.

$$t^{2}=\frac{2000}{193}$$

Take the square root of both sides of the equation.

$$t=\frac{20\sqrt{965}}{193} t=-\frac{20\sqrt{965}}{193}$$

Steps Using the Quadratic Formula

Expand \frac{3.86}{2} by multiplying both numerator and the denominator by 100.

$$20=\frac{386}{200}t^{2}$$

Reduce the fraction \frac{386}{200} to lowest terms by extracting and canceling out 2.

$$20=\frac{193}{100}t^{2}$$

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

$$\frac{193}{100}t^{2}=20$$

Subtract 20 from both sides.

$$\frac{193}{100}t^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{193}{100} for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{193}{100}\left(-20\right)}}{2\times \frac{193}{100}}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times \frac{193}{100}\left(-20\right)}}{2\times \frac{193}{100}}$$

Multiply -4 times \frac{193}{100}.

$$t=\frac{0±\sqrt{-\frac{193}{25}\left(-20\right)}}{2\times \frac{193}{100}}$$

Multiply -\frac{193}{25} times -20.

$$t=\frac{0±\sqrt{\frac{772}{5}}}{2\times \frac{193}{100}}$$

Take the square root of \frac{772}{5}.

$$t=\frac{0±\frac{2\sqrt{965}}{5}}{2\times \frac{193}{100}}$$

Multiply 2 times \frac{193}{100}.

$$t=\frac{0±\frac{2\sqrt{965}}{5}}{\frac{193}{50}}$$

Now solve the equation t=\frac{0±\frac{2\sqrt{965}}{5}}{\frac{193}{50}} when ± is plus.

$$t=\frac{20\sqrt{965}}{193}$$

Now solve the equation t=\frac{0±\frac{2\sqrt{965}}{5}}{\frac{193}{50}} when ± is minus.

$$t=-\frac{20\sqrt{965}}{193}$$

The equation is now solved.

$$t=\frac{20\sqrt{965}}{193} t=-\frac{20\sqrt{965}}{193}$$