n^2-12n=89

Solution for n^2-12n=89 equation:

n^2-12n=89

We move all terms to the left:

n^2-12n-(89)=0

a = 1; b = -12; c = -89;
Δ = b2-4ac
Δ = -122-4·1·(-89)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{5}}{2*1}=\frac{12-10\sqrt{5}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{5}}{2*1}=\frac{12+10\sqrt{5}}{2}
$