n2-6n-30=0

Solution for n2-6n-30=0 equation:

n2-6n-30=0

We add all the numbers together, and all the variables

n^2-6n-30=0

a = 1; b = -6; c = -30;
Δ = b2-4ac
Δ = -62-4·1·(-30)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*1}=\frac{6-2\sqrt{39}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*1}=\frac{6+2\sqrt{39}}{2}
$