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1/3*z=12
We move all terms to the left:
1/3*z-(12)=0
Domain of the equation: 3*z!=0We multiply all the terms by the denominator
z!=0/1
z!=0
z∈R
-12*3*z+1=0
Wy multiply elements
-36z*z+1=0
Wy multiply elements
-36z^2+1=0
a = -36; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-36)·1
Δ = 144
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{144}=12$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-36}=\frac{-12}{-72} =1/6 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-36}=\frac{12}{-72} =-1/6 $
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