(3a-1)(2a+1)=11

Solution for (3a-1)(2a+1)=11 equation:

(3a-1)(2a+1)=11

We move all terms to the left:

(3a-1)(2a+1)-(11)=0

We multiply parentheses ..

(+6a^2+3a-2a-1)-11=0

We get rid of parentheses

6a^2+3a-2a-1-11=0

We add all the numbers together, and all the variables

6a^2+a-12=0

a = 6; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·6·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*6}=\frac{-18}{12}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*6}=\frac{16}{12}
=1+1/3
$