x(40-2x)=150

Solution for x(40-2x)=150 equation:

x(40-2x)=150

We move all terms to the left:

x(40-2x)-(150)=0

We add all the numbers together, and all the variables

x(-2x+40)-150=0

We multiply parentheses

-2x^2+40x-150=0

a = -2; b = 40; c = -150;
Δ = b2-4ac
Δ = 402-4·(-2)·(-150)
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{-(40)-20}{2*-2}=\frac{-60}{-4}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20}{2*-2}=\frac{-20}{-4}
=+5
$