n^2-20n-12=0

Solution for n^2-20n-12=0 equation:

n^2-20n-12=0

a = 1; b = -20; c = -12;
Δ = b2-4ac
Δ = -202-4·1·(-12)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{7}}{2*1}=\frac{20-8\sqrt{7}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{7}}{2*1}=\frac{20+8\sqrt{7}}{2}
$