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9x^2-54x-81=0
a = 9; b = -54; c = -81;
Δ = b2-4ac
Δ = -542-4·9·(-81)
Δ = 5832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5832}=\sqrt{2916*2}=\sqrt{2916}*\sqrt{2}=54\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54\sqrt{2}}{2*9}=\frac{54-54\sqrt{2}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54\sqrt{2}}{2*9}=\frac{54+54\sqrt{2}}{18} $
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