8/6x-4x=1

Solution for 8/6x-4x=1 equation:

8/6x-4x=1

We move all terms to the left:

8/6x-4x-(1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+8/6x-1=0

We multiply all the terms by the denominator


-4x*6x-1*6x+8=0

Wy multiply elements

-24x^2-6x+8=0

a = -24; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-24)·8
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{201}}{2*-24}=\frac{6-2\sqrt{201}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{201}}{2*-24}=\frac{6+2\sqrt{201}}{-48}
$