1/4x=1/12x-3

Solution for 1/4x=1/12x-3 equation:

1/4x=1/12x-3

We move all terms to the left:

1/4x-(1/12x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x-3)!=0

x∈R


We get rid of parentheses

1/4x-1/12x+3=0

We calculate fractions


12x/48x^2+(-4x)/48x^2+3=0

We multiply all the terms by the denominator


12x+(-4x)+3*48x^2=0

Wy multiply elements

144x^2+12x+(-4x)=0

We get rid of parentheses

144x^2+12x-4x=0

We add all the numbers together, and all the variables

144x^2+8x=0

a = 144; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·144·0
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*144}=\frac{-16}{288}
=-1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*144}=\frac{0}{288}
=0
$