x(x+2)=482

Solution for x(x+2)=482 equation:

x(x+2)=482

We move all terms to the left:

x(x+2)-(482)=0

We multiply parentheses

x^2+2x-482=0

a = 1; b = 2; c = -482;
Δ = b2-4ac
Δ = 22-4·1·(-482)
Δ = 1932
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:

$\sqrt{\Delta}=\sqrt{1932}=\sqrt{4*483}=\sqrt{4}*\sqrt{483}=2\sqrt{483}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{483}}{2*1}=\frac{-2-2\sqrt{483}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{483}}{2*1}=\frac{-2+2\sqrt{483}}{2}
$