# What is the quadratic formula for 2x^2 - 3x - 5 = 0?

Aug 4, 2018

$x = \frac{5}{2}$ and $- 1$

#### Explanation:

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

The quadratic formula is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

This equation is in standard quadratic form, so we know that:
$a = 2$, $b = - 3$, and $c = - 5$.

Plug them into the equation and solve for $x$:
$x = \frac{- \left(- 3\right) \pm \sqrt{{\left(- 3\right)}^{2} - 4 \left(2\right) \left(- 5\right)}}{2 \left(2\right)}$

$x = \frac{3 \pm \sqrt{9 + 40}}{4}$

$x = \frac{3 \pm \sqrt{49}}{4}$

$x = \frac{3 \pm 7}{4}$

$x = \frac{10}{4}$ and $- \frac{4}{4}$

$x = \frac{5}{2}$ and $- 1$

Hope this helps!