x(x+2)=992

Solution for x(x+2)=992 equation:

x(x+2)=992

We move all terms to the left:

x(x+2)-(992)=0

We multiply parentheses

x^2+2x-992=0

a = 1; b = 2; c = -992;
Δ = b2-4ac
Δ = 22-4·1·(-992)
Δ = 3972
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:

$\sqrt{\Delta}=\sqrt{3972}=\sqrt{4*993}=\sqrt{4}*\sqrt{993}=2\sqrt{993}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{993}}{2*1}=\frac{-2-2\sqrt{993}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{993}}{2*1}=\frac{-2+2\sqrt{993}}{2}
$