# How do you use the quadratic formula to find both solutions to the quadratic equation 3x^2 + 4x = 6?

Jul 8, 2015

$x = \frac{\sqrt{22} - 2}{3}$
or
$x = - \frac{\sqrt{22} + 2}{3}$

#### Explanation:

$3 {x}^{2} + 4 x = 6$
is equivalent to
$\textcolor{w h i t e}{\text{XXXX}}$$3 {x}^{2} + 4 x - 6 = 0$

which is in the standard form
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} + b x + c = 0$
with roots based on the quadratic formula at
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

with $a = 3$, $b = 4$, and $c = - 6$ (from above)

this becomes
$\textcolor{w h i t e}{\text{XXXX}}$x = (-4+-sqrt(4^2-4(3)(-6)))/(2(3)

$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- 4 \pm \sqrt{16 + 72}}{6}$

$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- 2 \pm \sqrt{22}}{3}$