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9z^2-54z+76=0
a = 9; b = -54; c = +76;
Δ = b2-4ac
Δ = -542-4·9·76
Δ = 180
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{5}}{2*9}=\frac{54-6\sqrt{5}}{18} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{5}}{2*9}=\frac{54+6\sqrt{5}}{18} $
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