x(x+4)=392^2

Solution for x(x+4)=392^2 equation:

x(x+4)=392^2

We move all terms to the left:

x(x+4)-(392^2)=0

We add all the numbers together, and all the variables

x(x+4)-153664=0

We multiply parentheses

x^2+4x-153664=0

a = 1; b = 4; c = -153664;
Δ = b2-4ac
Δ = 42-4·1·(-153664)
Δ = 614672
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:

$\sqrt{\Delta}=\sqrt{614672}=\sqrt{16*38417}=\sqrt{16}*\sqrt{38417}=4\sqrt{38417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{38417}}{2*1}=\frac{-4-4\sqrt{38417}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{38417}}{2*1}=\frac{-4+4\sqrt{38417}}{2}
$