n^2-n=37830

Solution for n^2-n=37830 equation:

n^2-n=37830

We move all terms to the left:

n^2-n-(37830)=0

We add all the numbers together, and all the variables

n^2-1n-37830=0

a = 1; b = -1; c = -37830;
Δ = b2-4ac
Δ = -12-4·1·(-37830)
Δ = 151321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{151321}=389$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-389}{2*1}=\frac{-388}{2}
=-194
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+389}{2*1}=\frac{390}{2}
=195
$