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

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

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

We move all terms to the left:

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

We multiply parentheses

21x^2+14x-(3x+2)=0

We get rid of parentheses

21x^2+14x-3x-2=0

We add all the numbers together, and all the variables

21x^2+11x-2=0

a = 21; b = 11; c = -2;
Δ = b2-4ac
Δ = 112-4·21·(-2)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-17}{2*21}=\frac{-28}{42}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+17}{2*21}=\frac{6}{42}
=1/7
$