n(n-11)=224

Solution for n(n-11)=224 equation:

n(n-11)=224

We move all terms to the left:

n(n-11)-(224)=0

We multiply parentheses

n^2-11n-224=0

a = 1; b = -11; c = -224;
Δ = b2-4ac
Δ = -112-4·1·(-224)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{113}}{2*1}=\frac{11-3\sqrt{113}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{113}}{2*1}=\frac{11+3\sqrt{113}}{2}
$