# How do you use the quadratic formula to solve 9x^2-6x+37=0?

Dec 20, 2016

$x = \frac{1}{3} \pm 2 i$

#### Explanation:

$9 {x}^{2} - 6 x + 37 = 0$

is in the form:

$a {x}^{2} + b x + c = 0$

with $a = 9$, $b = - 6$ and $c = 37$

This has zeros given by the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\textcolor{w h i t e}{x} = \frac{6 \pm \sqrt{{\left(- 6\right)}^{2} - 4 \left(9\right) \left(37\right)}}{2 \left(9\right)}$

$\textcolor{w h i t e}{x} = \frac{6 \pm \sqrt{36 - 36 \left(37\right)}}{18}$

$\textcolor{w h i t e}{x} = \frac{6 \pm \sqrt{36 \left(1 - 37\right)}}{18}$

$\textcolor{w h i t e}{x} = \frac{6 \pm \sqrt{- {36}^{2}}}{18}$

$\textcolor{w h i t e}{x} = \frac{6 \pm 36 i}{18}$

$\textcolor{w h i t e}{x} = \frac{1}{3} \pm 2 i$