36=4x(20+x)

Solution for 36=4x(20+x) equation:

36=4x(20+x)

We move all terms to the left:

36-(4x(20+x))=0

We add all the numbers together, and all the variables

-(4x(x+20))+36=0


We calculate terms in parentheses: -(4x(x+20)), so:

4x(x+20)

We multiply parentheses

4x^2+80x

Back to the equation:

-(4x^2+80x)


We get rid of parentheses

-4x^2-80x+36=0

a = -4; b = -80; c = +36;
Δ = b2-4ac
Δ = -802-4·(-4)·36
Δ = 6976
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:

$\sqrt{\Delta}=\sqrt{6976}=\sqrt{64*109}=\sqrt{64}*\sqrt{109}=8\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{109}}{2*-4}=\frac{80-8\sqrt{109}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{109}}{2*-4}=\frac{80+8\sqrt{109}}{-8}
$