2(x+4)8x=14

Solution for 2(x+4)8x=14 equation:

2(x+4)8x=14

We move all terms to the left:

2(x+4)8x-(14)=0

We multiply parentheses

16x^2+64x-14=0

a = 16; b = 64; c = -14;
Δ = b2-4ac
Δ = 642-4·16·(-14)
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{78}}{2*16}=\frac{-64-8\sqrt{78}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{78}}{2*16}=\frac{-64+8\sqrt{78}}{32}
$