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5z+1=z^2
We move all terms to the left:
5z+1-(z^2)=0
determiningTheFunctionDomain -z^2+5z+1=0
We add all the numbers together, and all the variables
-1z^2+5z+1=0
a = -1; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-1)·1
Δ = 29
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{-(5)-\sqrt{29}}{2*-1}=\frac{-5-\sqrt{29}}{-2} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{29}}{2*-1}=\frac{-5+\sqrt{29}}{-2} $
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