2(2x+4)x=x+16

Solution for 2(2x+4)x=x+16 equation:

2(2x+4)x=x+16

We move all terms to the left:

2(2x+4)x-(x+16)=0

We multiply parentheses

4x^2+8x-(x+16)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+7x-16=0

a = 4; b = 7; c = -16;
Δ = b2-4ac
Δ = 72-4·4·(-16)
Δ = 305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{305}}{2*4}=\frac{-7-\sqrt{305}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{305}}{2*4}=\frac{-7+\sqrt{305}}{8}
$