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20(5z)-(1/2)z=234
We move all terms to the left:
20(5z)-(1/2)z-(234)=0
Domain of the equation: 2)z!=0We add all the numbers together, and all the variables
z!=0/1
z!=0
z∈R
205z-(+1/2)z-234=0
We multiply parentheses
-z^2+205z-234=0
We add all the numbers together, and all the variables
-1z^2+205z-234=0
a = -1; b = 205; c = -234;
Δ = b2-4ac
Δ = 2052-4·(-1)·(-234)
Δ = 41089
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(205)-\sqrt{41089}}{2*-1}=\frac{-205-\sqrt{41089}}{-2} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(205)+\sqrt{41089}}{2*-1}=\frac{-205+\sqrt{41089}}{-2} $
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