X(x+2)=41

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

X(X+2)=41

We move all terms to the left:

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

We multiply parentheses

X^2+2X-41=0

a = 1; b = 2; c = -41;
Δ = b2-4ac
Δ = 22-4·1·(-41)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{42}}{2*1}=\frac{-2-2\sqrt{42}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{42}}{2*1}=\frac{-2+2\sqrt{42}}{2}
$