2/3z+1/6z=1/4

Solution for 2/3z+1/6z=1/4 equation:

2/3z+1/6z=1/4

We move all terms to the left:

2/3z+1/6z-(1/4)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R



Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R


We add all the numbers together, and all the variables

2/3z+1/6z-(+1/4)=0

We get rid of parentheses

2/3z+1/6z-1/4=0

We calculate fractions


(-108z^2)/288z^2+192z/288z^2+48z/288z^2=0

We multiply all the terms by the denominator


(-108z^2)+192z+48z=0

We add all the numbers together, and all the variables

(-108z^2)+240z=0

We get rid of parentheses

-108z^2+240z=0

a = -108; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-108)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-108}=\frac{-480}{-216}
=2+2/9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-108}=\frac{0}{-216}
=0
$