X(x+4)=23

Solution for X(x+4)=23 equation:

X(X+4)=23

We move all terms to the left:

X(X+4)-(23)=0

We multiply parentheses

X^2+4X-23=0

a = 1; b = 4; c = -23;
Δ = b2-4ac
Δ = 42-4·1·(-23)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{3}}{2*1}=\frac{-4-6\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{3}}{2*1}=\frac{-4+6\sqrt{3}}{2}
$