# How do you solve 2x² + 5x = -3?

Apr 14, 2016

The solutions are:
$x = - 1$

$x = - \frac{3}{2}$

#### Explanation:

$2 {x}^{2} + 5 x = - 3$

$2 {x}^{2} + 5 x + 3 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:

$a = 2 , b = 5 , c = 3$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(5\right)}^{2} - \left(4 \cdot 2 \cdot 3\right)$

$= 25 - 24 = 1$

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

$x = \left(\frac{- 5 \pm \sqrt{1}}{2 \cdot 2}\right) = \frac{- 5 \pm 1}{4}$

The solutions are:
$x = \frac{- 5 + 1}{4} = - \frac{4}{4} = - 1$

$x = \frac{- 5 - 1}{4} = - \frac{6}{4} = - \frac{3}{2}$