20n^2+180n-6775=0

Solution for 20n^2+180n-6775=0 equation:

20n^2+180n-6775=0

a = 20; b = 180; c = -6775;
Δ = b2-4ac
Δ = 1802-4·20·(-6775)
Δ = 574400
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:

$\sqrt{\Delta}=\sqrt{574400}=\sqrt{1600*359}=\sqrt{1600}*\sqrt{359}=40\sqrt{359}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-40\sqrt{359}}{2*20}=\frac{-180-40\sqrt{359}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+40\sqrt{359}}{2*20}=\frac{-180+40\sqrt{359}}{40}
$