x(x+3)=504

Solution for x(x+3)=504 equation:

x(x+3)=504

We move all terms to the left:

x(x+3)-(504)=0

We multiply parentheses

x^2+3x-504=0

a = 1; b = 3; c = -504;
Δ = b2-4ac
Δ = 32-4·1·(-504)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-45}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+45}{2*1}=\frac{42}{2}
=21
$