Solve 0=-16t^2+305

$$0 = - 16 t ^ { 2 } + 305$$

Solve for t

$$t = \frac{\sqrt{305}}{4} \approx 4.366062299$$

$$t = -\frac{\sqrt{305}}{4} \approx -4.366062299$$

Steps by Finding Square Root

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

$$-16t^{2}+305=0$$

Subtract 305 from both sides. Anything subtracted from zero gives its negation.

$$-16t^{2}=-305$$

Divide both sides by -16.

$$t^{2}=\frac{-305}{-16}$$

Fraction \frac{-305}{-16} can be simplified to \frac{305}{16} by removing the negative sign from both the numerator and the denominator.

$$t^{2}=\frac{305}{16}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{305}}{4} t=-\frac{\sqrt{305}}{4}$$

Steps Using the Quadratic Formula

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

$$-16t^{2}+305=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 305 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 305}}{2\left(-16\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-16\right)\times 305}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$t=\frac{0±\sqrt{64\times 305}}{2\left(-16\right)}$$

Multiply 64 times 305.

$$t=\frac{0±\sqrt{19520}}{2\left(-16\right)}$$

Take the square root of 19520.

$$t=\frac{0±8\sqrt{305}}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{0±8\sqrt{305}}{-32}$$

Now solve the equation t=\frac{0±8\sqrt{305}}{-32} when ± is plus.

$$t=-\frac{\sqrt{305}}{4}$$

Now solve the equation t=\frac{0±8\sqrt{305}}{-32} when ± is minus.

$$t=\frac{\sqrt{305}}{4}$$

The equation is now solved.

$$t=-\frac{\sqrt{305}}{4} t=\frac{\sqrt{305}}{4}$$