X(x+2)+3=41

Solution for X(x+2)+3=41 equation:

X(X+2)+3=41

We move all terms to the left:

X(X+2)+3-(41)=0

We add all the numbers together, and all the variables

X(X+2)-38=0

We multiply parentheses

X^2+2X-38=0

a = 1; b = 2; c = -38;
Δ = b2-4ac
Δ = 22-4·1·(-38)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{39}}{2*1}=\frac{-2-2\sqrt{39}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{39}}{2*1}=\frac{-2+2\sqrt{39}}{2}
$