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

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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 $

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