20-1/3z=1/2z

Solution for 20-1/3z=1/2z equation:

20-1/3z=1/2z

We move all terms to the left:

20-1/3z-(1/2z)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R



Domain of the equation: 2z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

-1/3z-(+1/2z)+20=0

We get rid of parentheses

-1/3z-1/2z+20=0

We calculate fractions


(-2z)/6z^2+(-3z)/6z^2+20=0

We multiply all the terms by the denominator


(-2z)+(-3z)+20*6z^2=0

Wy multiply elements

120z^2+(-2z)+(-3z)=0

We get rid of parentheses

120z^2-2z-3z=0

We add all the numbers together, and all the variables

120z^2-5z=0

a = 120; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·120·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*120}=\frac{0}{240}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*120}=\frac{10}{240}
=1/24
$