(2x+9)(6x-7)=66

Solution for (2x+9)(6x-7)=66 equation:

(2x+9)(6x-7)=66

We move all terms to the left:

(2x+9)(6x-7)-(66)=0

We multiply parentheses ..

(+12x^2-14x+54x-63)-66=0

We get rid of parentheses

12x^2-14x+54x-63-66=0

We add all the numbers together, and all the variables

12x^2+40x-129=0

a = 12; b = 40; c = -129;
Δ = b2-4ac
Δ = 402-4·12·(-129)
Δ = 7792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7792}=\sqrt{16*487}=\sqrt{16}*\sqrt{487}=4\sqrt{487}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{487}}{2*12}=\frac{-40-4\sqrt{487}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{487}}{2*12}=\frac{-40+4\sqrt{487}}{24}
$