19/6x-1=1/4x

Solution for 19/6x-1=1/4x equation:

19/6x-1=1/4x

We move all terms to the left:

19/6x-1-(1/4x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

19/6x-(+1/4x)-1=0

We get rid of parentheses

19/6x-1/4x-1=0

We calculate fractions


76x/24x^2+(-6x)/24x^2-1=0

We multiply all the terms by the denominator


76x+(-6x)-1*24x^2=0

Wy multiply elements

-24x^2+76x+(-6x)=0

We get rid of parentheses

-24x^2+76x-6x=0

We add all the numbers together, and all the variables

-24x^2+70x=0

a = -24; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-24)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*-24}=\frac{-140}{-48}
=2+11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-24}=\frac{0}{-48}
=0
$