4x(4+6x)=6-8(3x+2)

Solution for 4x(4+6x)=6-8(3x+2) equation:

4x(4+6x)=6-8(3x+2)

We move all terms to the left:

4x(4+6x)-(6-8(3x+2))=0

We add all the numbers together, and all the variables

4x(6x+4)-(6-8(3x+2))=0

We multiply parentheses

24x^2+16x-(6-8(3x+2))=0


We calculate terms in parentheses: -(6-8(3x+2)), so:

6-8(3x+2)

determiningTheFunctionDomain
-8(3x+2)+6

We multiply parentheses

-24x-16+6

We add all the numbers together, and all the variables

-24x-10

Back to the equation:

-(-24x-10)


We get rid of parentheses

24x^2+16x+24x+10=0

We add all the numbers together, and all the variables

24x^2+40x+10=0

a = 24; b = 40; c = +10;
Δ = b2-4ac
Δ = 402-4·24·10
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{10}}{2*24}=\frac{-40-8\sqrt{10}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{10}}{2*24}=\frac{-40+8\sqrt{10}}{48}
$