4(3x-1)9x=11

Solution for 4(3x-1)9x=11 equation:

4(3x-1)9x=11

We move all terms to the left:

4(3x-1)9x-(11)=0

We multiply parentheses

108x^2-36x-11=0

a = 108; b = -36; c = -11;
Δ = b2-4ac
Δ = -362-4·108·(-11)
Δ = 6048
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:

$\sqrt{\Delta}=\sqrt{6048}=\sqrt{144*42}=\sqrt{144}*\sqrt{42}=12\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{42}}{2*108}=\frac{36-12\sqrt{42}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{42}}{2*108}=\frac{36+12\sqrt{42}}{216}
$