(3x+1)(2x+9)=2

Solution for (3x+1)(2x+9)=2 equation:

(3x+1)(2x+9)=2

We move all terms to the left:

(3x+1)(2x+9)-(2)=0

We multiply parentheses ..

(+6x^2+27x+2x+9)-2=0

We get rid of parentheses

6x^2+27x+2x+9-2=0

We add all the numbers together, and all the variables

6x^2+29x+7=0

a = 6; b = 29; c = +7;
Δ = b2-4ac
Δ = 292-4·6·7
Δ = 673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{673}}{2*6}=\frac{-29-\sqrt{673}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{673}}{2*6}=\frac{-29+\sqrt{673}}{12}
$