(4x+9)(3x-1)=2

Solution for (4x+9)(3x-1)=2 equation:

(4x+9)(3x-1)=2

We move all terms to the left:

(4x+9)(3x-1)-(2)=0

We multiply parentheses ..

(+12x^2-4x+27x-9)-2=0

We get rid of parentheses

12x^2-4x+27x-9-2=0

We add all the numbers together, and all the variables

12x^2+23x-11=0

a = 12; b = 23; c = -11;
Δ = b2-4ac
Δ = 232-4·12·(-11)
Δ = 1057
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{-(23)-\sqrt{1057}}{2*12}=\frac{-23-\sqrt{1057}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{1057}}{2*12}=\frac{-23+\sqrt{1057}}{24}
$