(4x+8)(6x-12)=x

Solution for (4x+8)(6x-12)=x equation:

(4x+8)(6x-12)=x

We move all terms to the left:

(4x+8)(6x-12)-(x)=0

We add all the numbers together, and all the variables

-1x+(4x+8)(6x-12)=0

We multiply parentheses ..

(+24x^2-48x+48x-96)-1x=0

We get rid of parentheses

24x^2-48x+48x-1x-96=0

We add all the numbers together, and all the variables

24x^2-1x-96=0

a = 24; b = -1; c = -96;
Δ = b2-4ac
Δ = -12-4·24·(-96)
Δ = 9217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{9217}}{2*24}=\frac{1-\sqrt{9217}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{9217}}{2*24}=\frac{1+\sqrt{9217}}{48}
$