Solve 17-1.5=1/2*9.8*t^2

$$17 - 1.5 = \frac { 1 } { 2 } \times 9.8 \times t ^ { 2 }$$

Solve for t

$$t = \frac{\sqrt{155}}{7} \approx 1.778557085$$

$$t = -\frac{\sqrt{155}}{7} \approx -1.778557085$$

Steps by Finding Square Root

Subtract 1.5 from 17 to get 15.5.

$$15.5=\frac{1}{2}\times 9.8t^{2}$$

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

$$15.5=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=15.5$$

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

$$t^{2}=15.5\times \frac{10}{49}$$

Multiply 15.5 and \frac{10}{49} to get \frac{155}{49}.

$$t^{2}=\frac{155}{49}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{155}}{7} t=-\frac{\sqrt{155}}{7}$$

Steps Using the Quadratic Formula

Subtract 1.5 from 17 to get 15.5.

$$15.5=\frac{1}{2}\times 9.8t^{2}$$

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

$$15.5=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=15.5$$

Subtract 15.5 from both sides.

$$\frac{49}{10}t^{2}-15.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{49}{10} for a, 0 for b, and -15.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-15.5\right)}}{2\times \frac{49}{10}}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-15.5\right)}}{2\times \frac{49}{10}}$$

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

$$t=\frac{0±\sqrt{-\frac{98}{5}\left(-15.5\right)}}{2\times \frac{49}{10}}$$

Multiply -\frac{98}{5} times -15.5 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$t=\frac{0±\sqrt{\frac{1519}{5}}}{2\times \frac{49}{10}}$$

Take the square root of \frac{1519}{5}.

$$t=\frac{0±\frac{7\sqrt{155}}{5}}{2\times \frac{49}{10}}$$

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

$$t=\frac{0±\frac{7\sqrt{155}}{5}}{\frac{49}{5}}$$

Now solve the equation t=\frac{0±\frac{7\sqrt{155}}{5}}{\frac{49}{5}} when ± is plus.

$$t=\frac{\sqrt{155}}{7}$$

Now solve the equation t=\frac{0±\frac{7\sqrt{155}}{5}}{\frac{49}{5}} when ± is minus.

$$t=-\frac{\sqrt{155}}{7}$$

The equation is now solved.

$$t=\frac{\sqrt{155}}{7} t=-\frac{\sqrt{155}}{7}$$