x/4x-3+6x=2

Solution for x/4x-3+6x=2 equation:

x/4x-3+6x=2

We move all terms to the left:

x/4x-3+6x-(2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

6x+x/4x-5=0

We multiply all the terms by the denominator


6x*4x+x-5*4x=0

We add all the numbers together, and all the variables

x+6x*4x-5*4x=0

Wy multiply elements

24x^2+x-20x=0

We add all the numbers together, and all the variables

24x^2-19x=0

a = 24; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·24·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*24}=\frac{38}{48}
=19/24
$