4(2x-3)6x=2

Solution for 4(2x-3)6x=2 equation:

4(2x-3)6x=2

We move all terms to the left:

4(2x-3)6x-(2)=0

We multiply parentheses

48x^2-72x-2=0

a = 48; b = -72; c = -2;
Δ = b2-4ac
Δ = -722-4·48·(-2)
Δ = 5568
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:

$\sqrt{\Delta}=\sqrt{5568}=\sqrt{64*87}=\sqrt{64}*\sqrt{87}=8\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{87}}{2*48}=\frac{72-8\sqrt{87}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{87}}{2*48}=\frac{72+8\sqrt{87}}{96}
$