x(x+3)=99

Solution for x(x+3)=99 equation:

x(x+3)=99

We move all terms to the left:

x(x+3)-(99)=0

We multiply parentheses

x^2+3x-99=0

a = 1; b = 3; c = -99;
Δ = b2-4ac
Δ = 32-4·1·(-99)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9\sqrt{5}}{2*1}=\frac{-3-9\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9\sqrt{5}}{2*1}=\frac{-3+9\sqrt{5}}{2}
$