# How do you solve n^ { 2} + 18n - 34= 0?

Mar 10, 2017

The solutions are $S = \left\{- 19.72 , 1.72\right\}$

#### Explanation:

We compare this equation to

$a {x}^{2} + b x + c = 0$

${n}^{2} + 18 n - 34 = 0$

We calculate the discriminant

$\Delta = {b}^{2} - 4 a c = {18}^{2} - 4 \cdot 1 \cdot \left(- 34\right)$

$= 324 + 136 = 460$

As $\Delta > 0$, there are 2 real solutions

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

$= \frac{- 18 \pm \sqrt{460}}{2}$

${n}_{1} = \frac{- 18 + 21.448}{2} = 1.72$

${n}_{2} = \frac{- 18 - 21.448}{2} = - 19.72$