3x(2x+1)+x-2=7x+1

Solution for 3x(2x+1)+x-2=7x+1 equation:

3x(2x+1)+x-2=7x+1

We move all terms to the left:

3x(2x+1)+x-2-(7x+1)=0

We add all the numbers together, and all the variables

x+3x(2x+1)-(7x+1)-2=0

We multiply parentheses

6x^2+x+3x-(7x+1)-2=0

We get rid of parentheses

6x^2+x+3x-7x-1-2=0

We add all the numbers together, and all the variables

6x^2-3x-3=0

a = 6; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·6·(-3)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*6}=\frac{12}{12}
=1
$