1/4x-13/12=1-1/6x

Solution for 1/4x-13/12=1-1/6x equation:

1/4x-13/12=1-1/6x

We move all terms to the left:

1/4x-13/12-(1-1/6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-1/6x+1)-13/12=0

We get rid of parentheses

1/4x+1/6x-1-13/12=0

We calculate fractions


(-1872x^2)/288x^2+72x/288x^2+48x/288x^2-1=0

We multiply all the terms by the denominator


(-1872x^2)+72x+48x-1*288x^2=0

We add all the numbers together, and all the variables

(-1872x^2)+120x-1*288x^2=0

Wy multiply elements

(-1872x^2)-288x^2+120x=0

We get rid of parentheses

-1872x^2-288x^2+120x=0

We add all the numbers together, and all the variables

-2160x^2+120x=0

a = -2160; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·(-2160)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*-2160}=\frac{-240}{-4320}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*-2160}=\frac{0}{-4320}
=0
$