100=20x(30+x)

Solution for 100=20x(30+x) equation:

100=20x(30+x)

We move all terms to the left:

100-(20x(30+x))=0

We add all the numbers together, and all the variables

-(20x(x+30))+100=0


We calculate terms in parentheses: -(20x(x+30)), so:

20x(x+30)

We multiply parentheses

20x^2+600x

Back to the equation:

-(20x^2+600x)


We get rid of parentheses

-20x^2-600x+100=0

a = -20; b = -600; c = +100;
Δ = b2-4ac
Δ = -6002-4·(-20)·100
Δ = 368000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{368000}=\sqrt{1600*230}=\sqrt{1600}*\sqrt{230}=40\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-40\sqrt{230}}{2*-20}=\frac{600-40\sqrt{230}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+40\sqrt{230}}{2*-20}=\frac{600+40\sqrt{230}}{-40}
$