3x,2(x+4)-2x-1=37

Solution for 3x,2(x+4)-2x-1=37 equation:

3x.2(x+4)-2x-1=37

We move all terms to the left:

3x.2(x+4)-2x-1-(37)=0

We add all the numbers together, and all the variables

-2x+3x.2(x+4)-38=0

We multiply parentheses

3x^2-2x+12x-38=0

We add all the numbers together, and all the variables

3x^2+10x-38=0

a = 3; b = 10; c = -38;
Δ = b2-4ac
Δ = 102-4·3·(-38)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{139}}{2*3}=\frac{-10-2\sqrt{139}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{139}}{2*3}=\frac{-10+2\sqrt{139}}{6}
$