3x,2(x+4)=2x+1

Solution for 3x,2(x+4)=2x+1 equation:

3x.2(x+4)=2x+1

We move all terms to the left:

3x.2(x+4)-(2x+1)=0

We multiply parentheses

3x^2+12x-(2x+1)=0

We get rid of parentheses

3x^2+12x-2x-1=0

We add all the numbers together, and all the variables

3x^2+10x-1=0

a = 3; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·3·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{7}}{2*3}=\frac{-10-4\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{7}}{2*3}=\frac{-10+4\sqrt{7}}{6}
$