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9r^2-9r-11=0
a = 9; b = -9; c = -11;
Δ = b2-4ac
Δ = -92-4·9·(-11)
Δ = 477
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{53}}{2*9}=\frac{9-3\sqrt{53}}{18} $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{53}}{2*9}=\frac{9+3\sqrt{53}}{18} $
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