# How do you solve x^2 +5x-7=0?

May 24, 2016

$x = \frac{- 5 \pm \sqrt{53}}{2}$

#### Explanation:

This quadratic equation is in the form $a {x}^{2} + b x + c = 0$ with $a = 1$, $b = 5$ and $c = - 7$.

It has discriminant $\Delta$ given by the formula:

$\Delta = {b}^{2} - 4 a c = {5}^{2} - \left(4 \cdot 1 \cdot - 7\right) = 25 + 28 = 53$

So $\Delta > 0$, but it is not a perfect square, so our quadratic equation has irrational roots.

We can find them using the quadratic formula:

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

$= \frac{- b \pm \sqrt{\Delta}}{2 a}$

$= \frac{- 5 \pm \sqrt{53}}{2}$