25x(180-x)=65

Solution for 25x(180-x)=65 equation:

25x(180-x)=65

We move all terms to the left:

25x(180-x)-(65)=0

We add all the numbers together, and all the variables

25x(-1x+180)-65=0

We multiply parentheses

-25x^2+4500x-65=0

a = -25; b = 4500; c = -65;
Δ = b2-4ac
Δ = 45002-4·(-25)·(-65)
Δ = 20243500
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:

$\sqrt{\Delta}=\sqrt{20243500}=\sqrt{100*202435}=\sqrt{100}*\sqrt{202435}=10\sqrt{202435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4500)-10\sqrt{202435}}{2*-25}=\frac{-4500-10\sqrt{202435}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4500)+10\sqrt{202435}}{2*-25}=\frac{-4500+10\sqrt{202435}}{-50}
$