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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

16x^2-12x-212=0

a = 16; b = -12; c = -212;
Δ = b2-4ac
Δ = -122-4·16·(-212)
Δ = 13712
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:

$\sqrt{\Delta}=\sqrt{13712}=\sqrt{16*857}=\sqrt{16}*\sqrt{857}=4\sqrt{857}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{857}}{2*16}=\frac{12-4\sqrt{857}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{857}}{2*16}=\frac{12+4\sqrt{857}}{32}
$