(n^2)-n=7.5

Solution for (n^2)-n=7.5 equation:

(n^2)-n=7.5

We move all terms to the left:

(n^2)-n-(7.5)=0

We add all the numbers together, and all the variables

n^2-1n-7.5=0

a = 1; b = -1; c = -7.5;
Δ = b2-4ac
Δ = -12-4·1·(-7.5)
Δ = 31
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{31}}{2*1}=\frac{1-\sqrt{31}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{31}}{2*1}=\frac{1+\sqrt{31}}{2}
$