x(x+4)=156

Solution for x(x+4)=156 equation:

x(x+4)=156

We move all terms to the left:

x(x+4)-(156)=0

We multiply parentheses

x^2+4x-156=0

a = 1; b = 4; c = -156;
Δ = b2-4ac
Δ = 42-4·1·(-156)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{10}}{2*1}=\frac{-4-8\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{10}}{2*1}=\frac{-4+8\sqrt{10}}{2}
$