4(x-4)6x=14

Solution for 4(x-4)6x=14 equation:

4(x-4)6x=14

We move all terms to the left:

4(x-4)6x-(14)=0

We multiply parentheses

24x^2-96x-14=0

a = 24; b = -96; c = -14;
Δ = b2-4ac
Δ = -962-4·24·(-14)
Δ = 10560
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:

$\sqrt{\Delta}=\sqrt{10560}=\sqrt{64*165}=\sqrt{64}*\sqrt{165}=8\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{165}}{2*24}=\frac{96-8\sqrt{165}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{165}}{2*24}=\frac{96+8\sqrt{165}}{48}
$