# How do you solve 5n^2-10n+59=0?

Feb 1, 2017

$x = 1 \pm \frac{3}{5} \sqrt{30} i$

#### Explanation:

You would apply the quadratic formula.

If the general form of the given equation is:

$a {x}^{2} + 2 n x + c$,

then

$x = \frac{- n \pm \sqrt{{\left(n\right)}^{2} - a c}}{a}$

Therefore:

$x = \frac{5 \pm \sqrt{{5}^{2} - 5 \cdot 59}}{5}$

$= \frac{5 \pm \sqrt{25 - 295}}{5}$

The solutions are complex, since the number under the square root is negative, then

$x = \frac{5 \pm \sqrt{- 270}}{5} = 1 \pm \frac{3}{5} \sqrt{30} i$