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

Solution for 6x+(12x/x-8)-12=0 equation:

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


Domain of the equation: x-8)!=0

x∈R


We get rid of parentheses

6x+12x/x-8-12=0

We multiply all the terms by the denominator


6x*x+12x-8*x-12*x=0

We add all the numbers together, and all the variables

-8x+6x*x=0

Wy multiply elements

6x^2-8x=0

a = 6; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·6·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*6}=\frac{16}{12}
=1+1/3
$