x(80-x)=1500

Solution for x(80-x)=1500 equation:

x(80-x)=1500

We move all terms to the left:

x(80-x)-(1500)=0

We add all the numbers together, and all the variables

x(-1x+80)-1500=0

We multiply parentheses

-1x^2+80x-1500=0

a = -1; b = 80; c = -1500;
Δ = b2-4ac
Δ = 802-4·(-1)·(-1500)
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{-(80)-20}{2*-1}=\frac{-100}{-2}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20}{2*-1}=\frac{-60}{-2}
=+30
$