2z/3z=15+z

Solution for 2z/3z=15+z equation:

2z/3z=15+z

We move all terms to the left:

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


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2z/3z-z-15=0

We multiply all the terms by the denominator


2z-z*3z-15*3z=0

Wy multiply elements

-3z^2+2z-45z=0

We add all the numbers together, and all the variables

-3z^2-43z=0

a = -3; b = -43; c = 0;
Δ = b2-4ac
Δ = -432-4·(-3)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-43}{2*-3}=\frac{0}{-6}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+43}{2*-3}=\frac{86}{-6}
=-14+1/3
$