# How do you solve 0= -16t^2+5t+30 ?

Aug 6, 2017

See a solution process below:

#### Explanation:

We can use the quadratic equation to solve this problem:

For $\textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$, the values of $x$ which are the solutions to the equation are given by:

$x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - \left(4 \textcolor{red}{a} \textcolor{g r e e n}{c}\right)}}{2 \cdot \textcolor{red}{a}}$

Substituting:

$\textcolor{red}{- 16}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{5}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{30}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{5} \pm \sqrt{{\textcolor{b l u e}{5}}^{2} - \left(4 \cdot \textcolor{red}{- 16} \cdot \textcolor{g r e e n}{30}\right)}}{2 \cdot \textcolor{red}{- 16}}$

$x = \frac{- \textcolor{b l u e}{5} \pm \sqrt{25 - \left(- 1920\right)}}{-} 32$

$x = \frac{- \textcolor{b l u e}{5} \pm \sqrt{25 + 1920}}{-} 32$

$x = \frac{- \textcolor{b l u e}{5} \pm \sqrt{1945}}{-} 32$

$x = \frac{\textcolor{b l u e}{5} \pm \sqrt{1945}}{32}$