8n(9n-5)=90

Solution for 8n(9n-5)=90 equation:

8n(9n-5)=90

We move all terms to the left:

8n(9n-5)-(90)=0

We multiply parentheses

72n^2-40n-90=0

a = 72; b = -40; c = -90;
Δ = b2-4ac
Δ = -402-4·72·(-90)
Δ = 27520
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:

$\sqrt{\Delta}=\sqrt{27520}=\sqrt{64*430}=\sqrt{64}*\sqrt{430}=8\sqrt{430}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{430}}{2*72}=\frac{40-8\sqrt{430}}{144}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{430}}{2*72}=\frac{40+8\sqrt{430}}{144}
$