3=(6x+4)2x

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

3=(6x+4)2x

We move all terms to the left:

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


We calculate terms in parentheses: -((6x+4)2x), so:

(6x+4)2x

We multiply parentheses

12x^2+8x

Back to the equation:

-(12x^2+8x)


We get rid of parentheses

-12x^2-8x+3=0

a = -12; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-12)·3
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*-12}=\frac{8-4\sqrt{13}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*-12}=\frac{8+4\sqrt{13}}{-24}
$