# How do you solve 3x^2 + 4 = -7x using the quadratic formula?

Aug 11, 2015

The solutions are
color(blue)(x=-4/3 ,x=-1

#### Explanation:

3x^2+4=−7x

$3 {x}^{2} + 7 x + 4 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 3 , b = 7 , c = 4$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(7\right)}^{2} - \left(4 \cdot 3 \cdot 4\right)$
$= 49 - 48$
$= 1$

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 7\right) \pm \sqrt{1}}{2 \cdot 3} = \frac{- 7 \pm \left(1\right)}{6}$

$x = \frac{- 7 - 1}{6} = - \frac{8}{6} = - \frac{4}{3}$

$x = \frac{- 7 + 1}{6} = - \frac{6}{6} = - 1$

The solutions are
color(blue)(x=-4/3 ,x=-1