180(n-2)n=25

Solution for 180(n-2)n=25 equation:

180(n-2)n=25

We move all terms to the left:

180(n-2)n-(25)=0

We multiply parentheses

180n^2-360n-25=0

a = 180; b = -360; c = -25;
Δ = b2-4ac
Δ = -3602-4·180·(-25)
Δ = 147600
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:

$\sqrt{\Delta}=\sqrt{147600}=\sqrt{3600*41}=\sqrt{3600}*\sqrt{41}=60\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-60\sqrt{41}}{2*180}=\frac{360-60\sqrt{41}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+60\sqrt{41}}{2*180}=\frac{360+60\sqrt{41}}{360}
$