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

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

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

We move all terms to the left:

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

We multiply parentheses

-24x^2-108x-(6-4(x-3))=0


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

6-4(x-3)

determiningTheFunctionDomain
-4(x-3)+6

We multiply parentheses

-4x+12+6

We add all the numbers together, and all the variables

-4x+18

Back to the equation:

-(-4x+18)


We get rid of parentheses

-24x^2-108x+4x-18=0

We add all the numbers together, and all the variables

-24x^2-104x-18=0

a = -24; b = -104; c = -18;
Δ = b2-4ac
Δ = -1042-4·(-24)·(-18)
Δ = 9088
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:

$\sqrt{\Delta}=\sqrt{9088}=\sqrt{64*142}=\sqrt{64}*\sqrt{142}=8\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-8\sqrt{142}}{2*-24}=\frac{104-8\sqrt{142}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+8\sqrt{142}}{2*-24}=\frac{104+8\sqrt{142}}{-48}
$