3(x-2)4x=21

Solution for 3(x-2)4x=21 equation:

3(x-2)4x=21

We move all terms to the left:

3(x-2)4x-(21)=0

We multiply parentheses

12x^2-24x-21=0

a = 12; b = -24; c = -21;
Δ = b2-4ac
Δ = -242-4·12·(-21)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{11}}{2*12}=\frac{24-12\sqrt{11}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{11}}{2*12}=\frac{24+12\sqrt{11}}{24}
$