3/5z-15=2+1/3z

Solution for 3/5z-15=2+1/3z equation:

3/5z-15=2+1/3z

We move all terms to the left:

3/5z-15-(2+1/3z)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 3z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

3/5z-(1/3z+2)-15=0

We get rid of parentheses

3/5z-1/3z-2-15=0

We calculate fractions


9z/15z^2+(-5z)/15z^2-2-15=0

We add all the numbers together, and all the variables

9z/15z^2+(-5z)/15z^2-17=0

We multiply all the terms by the denominator


9z+(-5z)-17*15z^2=0

Wy multiply elements

-255z^2+9z+(-5z)=0

We get rid of parentheses

-255z^2+9z-5z=0

We add all the numbers together, and all the variables

-255z^2+4z=0

a = -255; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-255)·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*-255}=\frac{-8}{-510}
=4/255
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-255}=\frac{0}{-510}
=0
$