180n^2-360n-174=0

Solution for 180n^2-360n-174=0 equation:

180n^2-360n-174=0

a = 180; b = -360; c = -174;
Δ = b2-4ac
Δ = -3602-4·180·(-174)
Δ = 254880
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:

$\sqrt{\Delta}=\sqrt{254880}=\sqrt{144*1770}=\sqrt{144}*\sqrt{1770}=12\sqrt{1770}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-12\sqrt{1770}}{2*180}=\frac{360-12\sqrt{1770}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+12\sqrt{1770}}{2*180}=\frac{360+12\sqrt{1770}}{360}
$