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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+6x^2+3x+4x+2)-1=0

We get rid of parentheses

6x^2+3x+4x+2-1=0

We add all the numbers together, and all the variables

6x^2+7x+1=0

a = 6; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·6·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*6}=\frac{-2}{12}
=-1/6
$