4x(2x+4)+4x=76

Solution for 4x(2x+4)+4x=76 equation:

4x(2x+4)+4x=76

We move all terms to the left:

4x(2x+4)+4x-(76)=0

We add all the numbers together, and all the variables

4x+4x(2x+4)-76=0

We multiply parentheses

8x^2+4x+16x-76=0

We add all the numbers together, and all the variables

8x^2+20x-76=0

a = 8; b = 20; c = -76;
Δ = b2-4ac
Δ = 202-4·8·(-76)
Δ = 2832
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:

$\sqrt{\Delta}=\sqrt{2832}=\sqrt{16*177}=\sqrt{16}*\sqrt{177}=4\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{177}}{2*8}=\frac{-20-4\sqrt{177}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{177}}{2*8}=\frac{-20+4\sqrt{177}}{16}
$