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9x^2-18x-66=0
a = 9; b = -18; c = -66;
Δ = b2-4ac
Δ = -182-4·9·(-66)
Δ = 2700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30\sqrt{3}}{2*9}=\frac{18-30\sqrt{3}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30\sqrt{3}}{2*9}=\frac{18+30\sqrt{3}}{18} $
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