4x(6x+2)-2(6+x)-20=12(1+2x)-2x

Solution for 4x(6x+2)-2(6+x)-20=12(1+2x)-2x equation:

4x(6x+2)-2(6+x)-20=12(1+2x)-2x

We move all terms to the left:

4x(6x+2)-2(6+x)-20-(12(1+2x)-2x)=0

We add all the numbers together, and all the variables

4x(6x+2)-2(x+6)-(12(2x+1)-2x)-20=0

We multiply parentheses

24x^2+8x-2x-(12(2x+1)-2x)-12-20=0


We calculate terms in parentheses: -(12(2x+1)-2x), so:

12(2x+1)-2x

We add all the numbers together, and all the variables

-2x+12(2x+1)

We multiply parentheses

-2x+24x+12

We add all the numbers together, and all the variables

22x+12

Back to the equation:

-(22x+12)


We add all the numbers together, and all the variables

24x^2+6x-(22x+12)-32=0

We get rid of parentheses

24x^2+6x-22x-12-32=0

We add all the numbers together, and all the variables

24x^2-16x-44=0

a = 24; b = -16; c = -44;
Δ = b2-4ac
Δ = -162-4·24·(-44)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{70}}{2*24}=\frac{16-8\sqrt{70}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{70}}{2*24}=\frac{16+8\sqrt{70}}{48}
$