(x-20)(50-x)=0

Solution for (x-20)(50-x)=0 equation:

(x-20)(50-x)=0

We add all the numbers together, and all the variables

(x-20)(-1x+50)=0

We multiply parentheses ..

(-1x^2+50x+20x-1000)=0

We get rid of parentheses

-1x^2+50x+20x-1000=0

We add all the numbers together, and all the variables

-1x^2+70x-1000=0

a = -1; b = 70; c = -1000;
Δ = b2-4ac
Δ = 702-4·(-1)·(-1000)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-30}{2*-1}=\frac{-100}{-2}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+30}{2*-1}=\frac{-40}{-2}
=+20
$