Solve 8=-10t^2+890

$$8 = - 10 t ^ { 2 } + 890$$

Solve for t

$$t = \frac{21 \sqrt{5}}{5} \approx 9.391485505$$

$$t = -\frac{21 \sqrt{5}}{5} \approx -9.391485505$$

Steps by Finding Square Root

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

$$-10t^{2}+890=8$$

Subtract 890 from both sides.

$$-10t^{2}=8-890$$

Subtract 890 from 8 to get -882.

$$-10t^{2}=-882$$

Divide both sides by -10.

$$t^{2}=\frac{-882}{-10}$$

Reduce the fraction \frac{-882}{-10} to lowest terms by extracting and canceling out -2.

$$t^{2}=\frac{441}{5}$$

Take the square root of both sides of the equation.

$$t=\frac{21\sqrt{5}}{5} t=-\frac{21\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

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

$$-10t^{2}+890=8$$

Subtract 8 from both sides.

$$-10t^{2}+890-8=0$$

Subtract 8 from 890 to get 882.

$$-10t^{2}+882=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -10 for a, 0 for b, and 882 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-10\right)\times 882}}{2\left(-10\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-10\right)\times 882}}{2\left(-10\right)}$$

Multiply -4 times -10.

$$t=\frac{0±\sqrt{40\times 882}}{2\left(-10\right)}$$

Multiply 40 times 882.

$$t=\frac{0±\sqrt{35280}}{2\left(-10\right)}$$

Take the square root of 35280.

$$t=\frac{0±84\sqrt{5}}{2\left(-10\right)}$$

Multiply 2 times -10.

$$t=\frac{0±84\sqrt{5}}{-20}$$

Now solve the equation t=\frac{0±84\sqrt{5}}{-20} when ± is plus.

$$t=-\frac{21\sqrt{5}}{5}$$

Now solve the equation t=\frac{0±84\sqrt{5}}{-20} when ± is minus.

$$t=\frac{21\sqrt{5}}{5}$$

The equation is now solved.

$$t=-\frac{21\sqrt{5}}{5} t=\frac{21\sqrt{5}}{5}$$