1/5z-1/2=1/6z

Solution for 1/5z-1/2=1/6z equation:

1/5z-1/2=1/6z

We move all terms to the left:

1/5z-1/2-(1/6z)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 6z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

1/5z-(+1/6z)-1/2=0

We get rid of parentheses

1/5z-1/6z-1/2=0

We calculate fractions


(-180z^2)/120z^2+24z/120z^2+(-20z)/120z^2=0

We multiply all the terms by the denominator


(-180z^2)+24z+(-20z)=0

We get rid of parentheses

-180z^2+24z-20z=0

We add all the numbers together, and all the variables

-180z^2+4z=0

a = -180; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-180)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-180}=\frac{-8}{-360}
=1/45
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-180}=\frac{0}{-360}
=0
$