(20+x)(30-x)=400

Solution for (20+x)(30-x)=400 equation:

(20+x)(30-x)=400

We move all terms to the left:

(20+x)(30-x)-(400)=0

We add all the numbers together, and all the variables

(x+20)(-1x+30)-400=0

We multiply parentheses ..

(-1x^2+30x-20x+600)-400=0

We get rid of parentheses

-1x^2+30x-20x+600-400=0

We add all the numbers together, and all the variables

-1x^2+10x+200=0

a = -1; b = 10; c = +200;
Δ = b2-4ac
Δ = 102-4·(-1)·200
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{-(10)-30}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*-1}=\frac{20}{-2}
=-10
$