(n)(n+2)=130

Solution for (n)(n+2)=130 equation:

(n)(n+2)=130

We move all terms to the left:

(n)(n+2)-(130)=0

We multiply parentheses

n^2+2n-130=0

a = 1; b = 2; c = -130;
Δ = b2-4ac
Δ = 22-4·1·(-130)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{131}}{2*1}=\frac{-2-2\sqrt{131}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{131}}{2*1}=\frac{-2+2\sqrt{131}}{2}
$