2(x+6)8x=10x-12

Solution for 2(x+6)8x=10x-12 equation:

2(x+6)8x=10x-12

We move all terms to the left:

2(x+6)8x-(10x-12)=0

We multiply parentheses

16x^2+96x-(10x-12)=0

We get rid of parentheses

16x^2+96x-10x+12=0

We add all the numbers together, and all the variables

16x^2+86x+12=0

a = 16; b = 86; c = +12;
Δ = b2-4ac
Δ = 862-4·16·12
Δ = 6628
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:

$\sqrt{\Delta}=\sqrt{6628}=\sqrt{4*1657}=\sqrt{4}*\sqrt{1657}=2\sqrt{1657}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{1657}}{2*16}=\frac{-86-2\sqrt{1657}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{1657}}{2*16}=\frac{-86+2\sqrt{1657}}{32}
$