n^2-20n+39=0

Solution for n^2-20n+39=0 equation:

n^2-20n+39=0

a = 1; b = -20; c = +39;
Δ = b2-4ac
Δ = -202-4·1·39
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{61}}{2*1}=\frac{20-2\sqrt{61}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{61}}{2*1}=\frac{20+2\sqrt{61}}{2}
$