4x(2+4x)=72

Solution for 4x(2+4x)=72 equation:

4x(2+4x)=72

We move all terms to the left:

4x(2+4x)-(72)=0

We add all the numbers together, and all the variables

4x(4x+2)-72=0

We multiply parentheses

16x^2+8x-72=0

a = 16; b = 8; c = -72;
Δ = b2-4ac
Δ = 82-4·16·(-72)
Δ = 4672
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:

$\sqrt{\Delta}=\sqrt{4672}=\sqrt{64*73}=\sqrt{64}*\sqrt{73}=8\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{73}}{2*16}=\frac{-8-8\sqrt{73}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{73}}{2*16}=\frac{-8+8\sqrt{73}}{32}
$