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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

11x-(3x(6x-12)-4(x-6))+6=0


We calculate terms in parentheses: -(3x(6x-12)-4(x-6)), so:

3x(6x-12)-4(x-6)

We multiply parentheses

18x^2-36x-4x+24

We add all the numbers together, and all the variables

18x^2-40x+24

Back to the equation:

-(18x^2-40x+24)


We get rid of parentheses

-18x^2+11x+40x-24+6=0

We add all the numbers together, and all the variables

-18x^2+51x-18=0

a = -18; b = 51; c = -18;
Δ = b2-4ac
Δ = 512-4·(-18)·(-18)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{145}}{2*-18}=\frac{-51-3\sqrt{145}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{145}}{2*-18}=\frac{-51+3\sqrt{145}}{-36}
$