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15-1/6z=1/3z
We move all terms to the left:
15-1/6z-(1/3z)=0
Domain of the equation: 6z!=0
z!=0/6
z!=0
z∈R
Domain of the equation: 3z)!=0We add all the numbers together, and all the variables
z!=0/1
z!=0
z∈R
-1/6z-(+1/3z)+15=0
We get rid of parentheses
-1/6z-1/3z+15=0
We calculate fractions
(-3z)/18z^2+(-6z)/18z^2+15=0
We multiply all the terms by the denominator
(-3z)+(-6z)+15*18z^2=0
Wy multiply elements
270z^2+(-3z)+(-6z)=0
We get rid of parentheses
270z^2-3z-6z=0
We add all the numbers together, and all the variables
270z^2-9z=0
a = 270; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·270·0
Δ = 81
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{81}=9$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*270}=\frac{0}{540} =0 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*270}=\frac{18}{540} =1/30 $
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