X(x+2)=4623

Solution for X(x+2)=4623 equation:

X(X+2)=4623

We move all terms to the left:

X(X+2)-(4623)=0

We multiply parentheses

X^2+2X-4623=0

a = 1; b = 2; c = -4623;
Δ = b2-4ac
Δ = 22-4·1·(-4623)
Δ = 18496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18496}=136$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-136}{2*1}=\frac{-138}{2}
=-69
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+136}{2*1}=\frac{134}{2}
=67
$