n^2-n=80

Solution for n^2-n=80 equation:

n^2-n=80

We move all terms to the left:

n^2-n-(80)=0

We add all the numbers together, and all the variables

n^2-1n-80=0

a = 1; b = -1; c = -80;
Δ = b2-4ac
Δ = -12-4·1·(-80)
Δ = 321
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{-(-1)-\sqrt{321}}{2*1}=\frac{1-\sqrt{321}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{321}}{2*1}=\frac{1+\sqrt{321}}{2}
$