6(x-3)2x=38

Solution for 6(x-3)2x=38 equation:

6(x-3)2x=38

We move all terms to the left:

6(x-3)2x-(38)=0

We multiply parentheses

12x^2-36x-38=0

a = 12; b = -36; c = -38;
Δ = b2-4ac
Δ = -362-4·12·(-38)
Δ = 3120
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:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{195}}{2*12}=\frac{36-4\sqrt{195}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{195}}{2*12}=\frac{36+4\sqrt{195}}{24}
$