90-5n=n2

Solution for 90-5n=n2 equation:

90-5n=n2

We move all terms to the left:

90-5n-(n2)=0

We add all the numbers together, and all the variables

-1n^2-5n+90=0

a = -1; b = -5; c = +90;
Δ = b2-4ac
Δ = -52-4·(-1)·90
Δ = 385
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{-(-5)-\sqrt{385}}{2*-1}=\frac{5-\sqrt{385}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{385}}{2*-1}=\frac{5+\sqrt{385}}{-2}
$