x(5+x)=156

Solution for x(5+x)=156 equation:

x(5+x)=156

We move all terms to the left:

x(5+x)-(156)=0

We add all the numbers together, and all the variables

x(x+5)-156=0

We multiply parentheses

x^2+5x-156=0

a = 1; b = 5; c = -156;
Δ = b2-4ac
Δ = 52-4·1·(-156)
Δ = 649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{649}}{2*1}=\frac{-5-\sqrt{649}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{649}}{2*1}=\frac{-5+\sqrt{649}}{2}
$