n2+5n=66

Solution for n2+5n=66 equation:

n2+5n=66

We move all terms to the left:

n2+5n-(66)=0

We add all the numbers together, and all the variables

n^2+5n-66=0

a = 1; b = 5; c = -66;
Δ = b2-4ac
Δ = 52-4·1·(-66)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*1}=\frac{-22}{2}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*1}=\frac{12}{2}
=6
$