n^2-20n-72=0

Solution for n^2-20n-72=0 equation:

n^2-20n-72=0

a = 1; b = -20; c = -72;
Δ = b2-4ac
Δ = -202-4·1·(-72)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{43}}{2*1}=\frac{20-4\sqrt{43}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{43}}{2*1}=\frac{20+4\sqrt{43}}{2}
$