-2x+6-3(2)(-2-4)-12x(7x-4)=9(2)

Solution for -2x+6-3(2)(-2-4)-12x(7x-4)=9(2) equation:

-2x+6-3(2)(-2-4)-12x(7x-4)=9(2)

We move all terms to the left:

-2x+6-3(2)(-2-4)-12x(7x-4)-(9(2))=0

determiningTheFunctionDomain
-2x-12x(7x-4)+6-32(-2-4)-92=0

We add all the numbers together, and all the variables

-2x-12x(7x-4)+6-92-32(-6)=0

We add all the numbers together, and all the variables

-2x-12x(7x-4)+106=0

We multiply parentheses

-84x^2-2x+48x+106=0

We add all the numbers together, and all the variables

-84x^2+46x+106=0

a = -84; b = 46; c = +106;
Δ = b2-4ac
Δ = 462-4·(-84)·106
Δ = 37732
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:

$\sqrt{\Delta}=\sqrt{37732}=\sqrt{4*9433}=\sqrt{4}*\sqrt{9433}=2\sqrt{9433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{9433}}{2*-84}=\frac{-46-2\sqrt{9433}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{9433}}{2*-84}=\frac{-46+2\sqrt{9433}}{-168}
$