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11x^2-9x-54=0
a = 11; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·11·(-54)
Δ = 2457
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2457}=\sqrt{9*273}=\sqrt{9}*\sqrt{273}=3\sqrt{273}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{273}}{2*11}=\frac{9-3\sqrt{273}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{273}}{2*11}=\frac{9+3\sqrt{273}}{22} $
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