n2-18n-30=0

Solution for n2-18n-30=0 equation:

n2-18n-30=0

We add all the numbers together, and all the variables

n^2-18n-30=0

a = 1; b = -18; c = -30;
Δ = b2-4ac
Δ = -182-4·1·(-30)
Δ = 444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*1}=\frac{18-2\sqrt{111}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*1}=\frac{18+2\sqrt{111}}{2}
$