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11x^2-72x+24=0
a = 11; b = -72; c = +24;
Δ = b2-4ac
Δ = -722-4·11·24
Δ = 4128
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4128}=\sqrt{16*258}=\sqrt{16}*\sqrt{258}=4\sqrt{258}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{258}}{2*11}=\frac{72-4\sqrt{258}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{258}}{2*11}=\frac{72+4\sqrt{258}}{22} $
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