x(30+x)=99

Solution for x(30+x)=99 equation:

x(30+x)=99

We move all terms to the left:

x(30+x)-(99)=0

We add all the numbers together, and all the variables

x(x+30)-99=0

We multiply parentheses

x^2+30x-99=0

a = 1; b = 30; c = -99;
Δ = b2-4ac
Δ = 302-4·1·(-99)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-36}{2*1}=\frac{-66}{2}
=-33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+36}{2*1}=\frac{6}{2}
=3
$