140=x*(20+x)

Solution for 140=x*(20+x) equation:

140=x(20+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(x+20))+140=0


We calculate terms in parentheses: -(x(x+20)), so:

x(x+20)

We multiply parentheses

x^2+20x

Back to the equation:

-(x^2+20x)


We get rid of parentheses

-x^2-20x+140=0

We add all the numbers together, and all the variables

-1x^2-20x+140=0

a = -1; b = -20; c = +140;
Δ = b2-4ac
Δ = -202-4·(-1)·140
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{15}}{2*-1}=\frac{20-8\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{15}}{2*-1}=\frac{20+8\sqrt{15}}{-2}
$