n^2-6n-39=0

Solution for n^2-6n-39=0 equation:

n^2-6n-39=0

a = 1; b = -6; c = -39;
Δ = b2-4ac
Δ = -62-4·1·(-39)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{3}}{2*1}=\frac{6-8\sqrt{3}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{3}}{2*1}=\frac{6+8\sqrt{3}}{2}
$