x(x+3)=15^2

Solution for x(x+3)=15^2 equation:

x(x+3)=15^2

We move all terms to the left:

x(x+3)-(15^2)=0

We add all the numbers together, and all the variables

x(x+3)-225=0

We multiply parentheses

x^2+3x-225=0

a = 1; b = 3; c = -225;
Δ = b2-4ac
Δ = 32-4·1·(-225)
Δ = 909
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:

$\sqrt{\Delta}=\sqrt{909}=\sqrt{9*101}=\sqrt{9}*\sqrt{101}=3\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{101}}{2*1}=\frac{-3-3\sqrt{101}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{101}}{2*1}=\frac{-3+3\sqrt{101}}{2}
$