x*(60-x)+(60-x)*x=1600

Solution for x*(60-x)+(60-x)*x=1600 equation:

x(60-x)+(60-x)*x=1600

We move all terms to the left:

x(60-x)+(60-x)*x-(1600)=0

We add all the numbers together, and all the variables

x(-1x+60)+(-1x+60)*x-1600=0

We multiply parentheses

-1x^2-1x^2+60x+60x-1600=0

We add all the numbers together, and all the variables

-2x^2+120x-1600=0

a = -2; b = 120; c = -1600;
Δ = b2-4ac
Δ = 1202-4·(-2)·(-1600)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40}{2*-2}=\frac{-160}{-4}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40}{2*-2}=\frac{-80}{-4}
=+20
$