n^2-3n=130

Solution for n^2-3n=130 equation:

n^2-3n=130

We move all terms to the left:

n^2-3n-(130)=0

a = 1; b = -3; c = -130;
Δ = b2-4ac
Δ = -32-4·1·(-130)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-23}{2*1}=\frac{-20}{2}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+23}{2*1}=\frac{26}{2}
=13
$