x/8x-12=6x

Solution for x/8x-12=6x equation:

x/8x-12=6x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-48x^2-95x=0

a = -48; b = -95; c = 0;
Δ = b2-4ac
Δ = -952-4·(-48)·0
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-95}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+95}{2*-48}=\frac{190}{-96}
=-1+47/48
$