36=4x(18+x)

Solution for 36=4x(18+x) equation:

36=4x(18+x)

We move all terms to the left:

36-(4x(18+x))=0

We add all the numbers together, and all the variables

-(4x(x+18))+36=0


We calculate terms in parentheses: -(4x(x+18)), so:

4x(x+18)

We multiply parentheses

4x^2+72x

Back to the equation:

-(4x^2+72x)


We get rid of parentheses

-4x^2-72x+36=0

a = -4; b = -72; c = +36;
Δ = b2-4ac
Δ = -722-4·(-4)·36
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{10}}{2*-4}=\frac{72-24\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{10}}{2*-4}=\frac{72+24\sqrt{10}}{-8}
$