3(2x-6)2x=13

Solution for 3(2x-6)2x=13 equation:

3(2x-6)2x=13

We move all terms to the left:

3(2x-6)2x-(13)=0

We multiply parentheses

12x^2-36x-13=0

a = 12; b = -36; c = -13;
Δ = b2-4ac
Δ = -362-4·12·(-13)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{30}}{2*12}=\frac{36-8\sqrt{30}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{30}}{2*12}=\frac{36+8\sqrt{30}}{24}
$