180=65x(x-5)

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

180=65x(x-5)

We move all terms to the left:

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


We calculate terms in parentheses: -(65x(x-5)), so:

65x(x-5)

We multiply parentheses

65x^2-325x

Back to the equation:

-(65x^2-325x)


We get rid of 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}
$