X*(x+1)=506

Solution for X*(x+1)=506 equation:

X(X+1)=506

We move all terms to the left:

X(X+1)-(506)=0

We multiply parentheses

X^2+X-506=0

a = 1; b = 1; c = -506;
Δ = b2-4ac
Δ = 12-4·1·(-506)
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{-(1)-45}{2*1}=\frac{-46}{2}
=-23
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+45}{2*1}=\frac{44}{2}
=22
$