x(x+2)=228

Solution for x(x+2)=228 equation:

x(x+2)=228

We move all terms to the left:

x(x+2)-(228)=0

We multiply parentheses

x^2+2x-228=0

a = 1; b = 2; c = -228;
Δ = b2-4ac
Δ = 22-4·1·(-228)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{229}}{2*1}=\frac{-2-2\sqrt{229}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{229}}{2*1}=\frac{-2+2\sqrt{229}}{2}
$