[x(x+1)=552

Solution for [x(x+1)=552 equation:

x(x+1)=552

We move all terms to the left:

x(x+1)-(552)=0

We multiply parentheses

x^2+x-552=0

a = 1; b = 1; c = -552;
Δ = b2-4ac
Δ = 12-4·1·(-552)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-47}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+47}{2*1}=\frac{46}{2}
=23
$