x(x-5)65=180

Solution for x(x-5)65=180 equation:

x(x-5)65=180

We move all terms to the left:

x(x-5)65-(180)=0

We multiply parentheses

65x^2-325x-180=0

a = 65; b = -325; c = -180;
Δ = b2-4ac
Δ = -3252-4·65·(-180)
Δ = 152425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{152425}=\sqrt{25*6097}=\sqrt{25}*\sqrt{6097}=5\sqrt{6097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-325)-5\sqrt{6097}}{2*65}=\frac{325-5\sqrt{6097}}{130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-325)+5\sqrt{6097}}{2*65}=\frac{325+5\sqrt{6097}}{130}
$