1/4x-2=6+5/12x

Solution for 1/4x-2=6+5/12x equation:

1/4x-2=6+5/12x

We move all terms to the left:

1/4x-2-(6+5/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(5/12x+6)-2=0

We get rid of parentheses

1/4x-5/12x-6-2=0

We calculate fractions


12x/48x^2+(-20x)/48x^2-6-2=0

We add all the numbers together, and all the variables

12x/48x^2+(-20x)/48x^2-8=0

We multiply all the terms by the denominator


12x+(-20x)-8*48x^2=0

Wy multiply elements

-384x^2+12x+(-20x)=0

We get rid of parentheses

-384x^2+12x-20x=0

We add all the numbers together, and all the variables

-384x^2-8x=0

a = -384; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-384)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-384}=\frac{0}{-768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-384}=\frac{16}{-768}
=-1/48
$