# How do you solve using the quadratic formula 2x^2 + 5x - 3 = 0?

May 14, 2015

$2 {x}^{2} + 5 x - 3 = 0$ is of the form $a {x}^{2} + b x + c = 0$ with $a = 2$, $b = 5$ and $c = - 3$.

The quadratic formula tells us that this has solutions:

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

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

$= \frac{- 5 \pm \sqrt{25 + 24}}{4}$

$= \frac{- 5 \pm \sqrt{49}}{4}$

$= \frac{- 5 \pm 7}{4}$

In other words, $x = \frac{1}{2}$ or $x = - 3$