# How do you solve using the quadratic formula for 4x^2+12x+5=117?

May 31, 2015

First subtract 117 from both sides to get:

$4 {x}^{2} + 12 x - 112 = 0$

Notice all the terms are divisible by $4$, so divide both sides by $4$ to get:

${x}^{2} + 3 x - 28 = 0$

This is in the form $a {x}^{2} + b x + c = 0$ with $a = 1$, $b = 3$, $c = - 28$

Then

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

$= \frac{- 3 \pm \sqrt{{3}^{2} - \left(4 \times 1 \times - 28\right)}}{2 \times 1}$

$= \frac{- 3 \pm \sqrt{9 + 112}}{2}$

$= \frac{- 3 \pm \sqrt{121}}{2}$

$= \frac{- 3 \pm \sqrt{{11}^{2}}}{2}$

$= \frac{- 3 \pm 11}{2}$

That is $x = - 7$ or $x = 4$