Solve 78=1/2*9.8t^2

$$78 = \frac { 1 } { 2 } \times 9.8 t ^ { 2 }$$

Solve for t

$$t = \frac{2 \sqrt{195}}{7} \approx 3.98978287$$

$$t = -\frac{2 \sqrt{195}}{7} \approx -3.98978287$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$78=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=78$$

Multiply both sides by \frac{10}{49}, the reciprocal of \frac{49}{10}.

$$t^{2}=78\times \frac{10}{49}$$

Multiply 78 and \frac{10}{49} to get \frac{780}{49}.

$$t^{2}=\frac{780}{49}$$

Take the square root of both sides of the equation.

$$t=\frac{2\sqrt{195}}{7} t=-\frac{2\sqrt{195}}{7}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$78=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=78$$

Subtract 78 from both sides.

$$\frac{49}{10}t^{2}-78=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{49}{10} for a, 0 for b, and -78 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-78\right)}}{2\times \frac{49}{10}}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-78\right)}}{2\times \frac{49}{10}}$$

Multiply -4 times \frac{49}{10}.

$$t=\frac{0±\sqrt{-\frac{98}{5}\left(-78\right)}}{2\times \frac{49}{10}}$$

Multiply -\frac{98}{5} times -78.

$$t=\frac{0±\sqrt{\frac{7644}{5}}}{2\times \frac{49}{10}}$$

Take the square root of \frac{7644}{5}.

$$t=\frac{0±\frac{14\sqrt{195}}{5}}{2\times \frac{49}{10}}$$

Multiply 2 times \frac{49}{10}.

$$t=\frac{0±\frac{14\sqrt{195}}{5}}{\frac{49}{5}}$$

Now solve the equation t=\frac{0±\frac{14\sqrt{195}}{5}}{\frac{49}{5}} when ± is plus.

$$t=\frac{2\sqrt{195}}{7}$$

Now solve the equation t=\frac{0±\frac{14\sqrt{195}}{5}}{\frac{49}{5}} when ± is minus.

$$t=-\frac{2\sqrt{195}}{7}$$

The equation is now solved.

$$t=\frac{2\sqrt{195}}{7} t=-\frac{2\sqrt{195}}{7}$$