n^2+10n=18

Solution for n^2+10n=18 equation:

n^2+10n=18

We move all terms to the left:

n^2+10n-(18)=0

a = 1; b = 10; c = -18;
Δ = b2-4ac
Δ = 102-4·1·(-18)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*1}=\frac{-10-2\sqrt{43}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*1}=\frac{-10+2\sqrt{43}}{2}
$