-1/12z+1/3=1/4z

Solution for -1/12z+1/3=1/4z equation:

-1/12z+1/3=1/4z

We move all terms to the left:

-1/12z+1/3-(1/4z)=0


Domain of the equation: 12z!=0

z!=0/12

z!=0

z∈R



Domain of the equation: 4z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

-1/12z-(+1/4z)+1/3=0

We get rid of parentheses

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

We calculate fractions


192z^2/432z^2+(-36z)/432z^2+(-108z)/432z^2=0

We multiply all the terms by the denominator


192z^2+(-36z)+(-108z)=0

We get rid of parentheses

192z^2-36z-108z=0

We add all the numbers together, and all the variables

192z^2-144z=0

a = 192; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·192·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*192}=\frac{0}{384}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*192}=\frac{288}{384}
=3/4
$