x(20+x)=196

Solution for x(20+x)=196 equation:

x(20+x)=196

We move all terms to the left:

x(20+x)-(196)=0

We add all the numbers together, and all the variables

x(x+20)-196=0

We multiply parentheses

x^2+20x-196=0

a = 1; b = 20; c = -196;
Δ = b2-4ac
Δ = 202-4·1·(-196)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{74}}{2*1}=\frac{-20-4\sqrt{74}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{74}}{2*1}=\frac{-20+4\sqrt{74}}{2}
$