2(4x-3)2x=2(7+5)+2x

Solution for 2(4x-3)2x=2(7+5)+2x equation:

2(4x-3)2x=2(7+5)+2x

We move all terms to the left:

2(4x-3)2x-(2(7+5)+2x)=0

We add all the numbers together, and all the variables

2(4x-3)2x-(212+2x)=0

We multiply parentheses

16x^2-12x-(212+2x)=0

We get rid of parentheses

16x^2-12x-2x-212=0

We add all the numbers together, and all the variables

16x^2-14x-212=0

a = 16; b = -14; c = -212;
Δ = b2-4ac
Δ = -142-4·16·(-212)
Δ = 13764
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:

$\sqrt{\Delta}=\sqrt{13764}=\sqrt{4*3441}=\sqrt{4}*\sqrt{3441}=2\sqrt{3441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{3441}}{2*16}=\frac{14-2\sqrt{3441}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{3441}}{2*16}=\frac{14+2\sqrt{3441}}{32}
$