# How do you use the quadratic formula to solve -6x^2+3x+2=3?

Mar 18, 2018

$\frac{1 \pm i \sqrt{15}}{4}$

#### Explanation:

The first thing we need to do before solving using the quadratic formula, is to get everything to one side, causing the equation to equal zero:

$- 6 {x}^{2} + 3 x + 2 = 3 \implies - 6 {x}^{2} + 3 x - 1 = 0$

Having this, we can now solve using the quadratic formula.

The quadratic formula is as follows:

$\frac{- \textcolor{red}{b} \pm \sqrt{{\textcolor{red}{b}}^{2} - 4 \textcolor{\mathmr{and} a n \ge}{a} \textcolor{b l u e}{c}}}{2 \textcolor{\mathmr{and} a n \ge}{a}}$

We derive each of these values from the quadratic:

$\textcolor{\mathmr{and} a n \ge}{a} {x}^{2} + \textcolor{red}{b} x + \textcolor{b l u e}{c}$ so " "color(orange)(a = -6" "color(red)(b = 3) " "color(blue)(c=-1)

Now we plug in our corresponding numbers:

(-3+-sqrt(3^2-4(-6)(-1)))/(2(-6)

$= \frac{- 3 \pm \sqrt{9 - 24}}{-} 12$

$= \frac{- 3 \pm \sqrt{- 15}}{-} 12$

$= \frac{1 \pm i \sqrt{15}}{4}$