X(x+1)=1x+576

Solution for X(x+1)=1x+576 equation:

X(X+1)=1X+576

We move all terms to the left:

X(X+1)-(1X+576)=0

We add all the numbers together, and all the variables

X(X+1)-(X+576)=0

We multiply parentheses

X^2+X-(X+576)=0

We get rid of parentheses

X^2+X-X-576=0

We add all the numbers together, and all the variables

X^2-576=0

a = 1; b = 0; c = -576;
Δ = b2-4ac
Δ = 02-4·1·(-576)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*1}=\frac{-48}{2}
=-24
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*1}=\frac{48}{2}
=24
$