X(x+2)=65

Solution for X(x+2)=65 equation:

X(X+2)=65

We move all terms to the left:

X(X+2)-(65)=0

We multiply parentheses

X^2+2X-65=0

a = 1; b = 2; c = -65;
Δ = b2-4ac
Δ = 22-4·1·(-65)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{66}}{2*1}=\frac{-2-2\sqrt{66}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{66}}{2*1}=\frac{-2+2\sqrt{66}}{2}
$