4x+2x(x+6)=36

Solution for 4x+2x(x+6)=36 equation:

4x+2x(x+6)=36

We move all terms to the left:

4x+2x(x+6)-(36)=0

We multiply parentheses

2x^2+4x+12x-36=0

We add all the numbers together, and all the variables

2x^2+16x-36=0

a = 2; b = 16; c = -36;
Δ = b2-4ac
Δ = 162-4·2·(-36)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{34}}{2*2}=\frac{-16-4\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{34}}{2*2}=\frac{-16+4\sqrt{34}}{4}
$