x(30+x)=8800

Solution for x(30+x)=8800 equation:

x(30+x)=8800

We move all terms to the left:

x(30+x)-(8800)=0

We add all the numbers together, and all the variables

x(x+30)-8800=0

We multiply parentheses

x^2+30x-8800=0

a = 1; b = 30; c = -8800;
Δ = b2-4ac
Δ = 302-4·1·(-8800)
Δ = 36100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36100}=190$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-190}{2*1}=\frac{-220}{2}
=-110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+190}{2*1}=\frac{160}{2}
=80
$