n^2+5n=64

Solution for n^2+5n=64 equation:

n^2+5n=64

We move all terms to the left:

n^2+5n-(64)=0

a = 1; b = 5; c = -64;
Δ = b2-4ac
Δ = 52-4·1·(-64)
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{281}}{2*1}=\frac{-5-\sqrt{281}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{281}}{2*1}=\frac{-5+\sqrt{281}}{2}
$