# How do you solve 2x² - 7x + 15 = 0?

Jun 26, 2015

Note that this equation has no Real roots. Complex roots can be determined using the quadratic formula.
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{7 + \sqrt{71} i}{4}$ or $x = \frac{7 - \sqrt{71} i}{4}$

#### Explanation:

The roots of a quadratic of the form
$\textcolor{w h i t e}{\text{XXXX}}$$a {x}^{2} + b x + c = 0$
can be determined using the quadratic formula:
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In this case:
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{7 \pm \sqrt{{\left(- 7\right)}^{2} - 4 \left(2\right) \left(15\right)}}{2 \left(2\right)}$

$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{7 \pm \sqrt{- 71}}{4}$

$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{7 + \sqrt{71} i}{4}$ or $x = \frac{7 - \sqrt{71} i}{4}$