90n^2-50n-20=0

Solution for 90n^2-50n-20=0 equation:

90n^2-50n-20=0

a = 90; b = -50; c = -20;
Δ = b2-4ac
Δ = -502-4·90·(-20)
Δ = 9700
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:

$\sqrt{\Delta}=\sqrt{9700}=\sqrt{100*97}=\sqrt{100}*\sqrt{97}=10\sqrt{97}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{97}}{2*90}=\frac{50-10\sqrt{97}}{180}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{97}}{2*90}=\frac{50+10\sqrt{97}}{180}
$