(x)(60-x)=800

Solution for (x)(60-x)=800 equation:

(x)(60-x)=800

We move all terms to the left:

(x)(60-x)-(800)=0

We add all the numbers together, and all the variables

x(-1x+60)-800=0

We multiply parentheses

-1x^2+60x-800=0

a = -1; b = 60; c = -800;
Δ = b2-4ac
Δ = 602-4·(-1)·(-800)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20}{2*-1}=\frac{-80}{-2}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20}{2*-1}=\frac{-40}{-2}
=+20
$