10n(n-3)=90

Solution for 10n(n-3)=90 equation:

10n(n-3)=90

We move all terms to the left:

10n(n-3)-(90)=0

We multiply parentheses

10n^2-30n-90=0

a = 10; b = -30; c = -90;
Δ = b2-4ac
Δ = -302-4·10·(-90)
Δ = 4500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30\sqrt{5}}{2*10}=\frac{30-30\sqrt{5}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30\sqrt{5}}{2*10}=\frac{30+30\sqrt{5}}{20}
$