6(3-x)2x=14

Solution for 6(3-x)2x=14 equation:

6(3-x)2x=14

We move all terms to the left:

6(3-x)2x-(14)=0

We add all the numbers together, and all the variables

6(-1x+3)2x-14=0

We multiply parentheses

-12x^2+36x-14=0

a = -12; b = 36; c = -14;
Δ = b2-4ac
Δ = 362-4·(-12)·(-14)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{39}}{2*-12}=\frac{-36-4\sqrt{39}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{39}}{2*-12}=\frac{-36+4\sqrt{39}}{-24}
$