# How do you solve using the quadratic formula 5x^2 – x + 12 = 0?

May 14, 2018

See a solution process below;

#### Explanation:

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:

$\textcolor{red}{5}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{- 1}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{12}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \left(\textcolor{b l u e}{- 1}\right) \pm \sqrt{{\textcolor{b l u e}{- 1}}^{2} - \left(4 \cdot \textcolor{red}{5} \cdot \textcolor{g r e e n}{12}\right)}}{2 \cdot \textcolor{red}{5}}$

$x = \frac{1 \pm \sqrt{1 - 240}}{10}$

$x = \frac{1 \pm \sqrt{- 239}}{10}$