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

Solution for 3(x+6)(2x-7)=9 equation:

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

We move all terms to the left:

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

We multiply parentheses ..

3(+2x^2-7x+12x-42)-9=0

We multiply parentheses

6x^2-21x+36x-126-9=0

We add all the numbers together, and all the variables

6x^2+15x-135=0

a = 6; b = 15; c = -135;
Δ = b2-4ac
Δ = 152-4·6·(-135)
Δ = 3465
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:

$\sqrt{\Delta}=\sqrt{3465}=\sqrt{9*385}=\sqrt{9}*\sqrt{385}=3\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{385}}{2*6}=\frac{-15-3\sqrt{385}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{385}}{2*6}=\frac{-15+3\sqrt{385}}{12}
$