(3x+1)(x-2)-3x=1

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

(3x+1)(x-2)-3x=1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+3x^2-6x+x-2)-3x-1=0

We get rid of parentheses

3x^2-6x+x-3x-2-1=0

We add all the numbers together, and all the variables

3x^2-8x-3=0

a = 3; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·3·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*3}=\frac{-2}{6}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*3}=\frac{18}{6}
=3
$