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9z^2=27
We move all terms to the left:
9z^2-(27)=0
a = 9; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·9·(-27)
Δ = 972
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*9}=\frac{0-18\sqrt{3}}{18} =-\frac{18\sqrt{3}}{18} =-\sqrt{3} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*9}=\frac{0+18\sqrt{3}}{18} =\frac{18\sqrt{3}}{18} =\sqrt{3} $
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