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11x^2+121x+218=0
a = 11; b = 121; c = +218;
Δ = b2-4ac
Δ = 1212-4·11·218
Δ = 5049
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-3\sqrt{561}}{2*11}=\frac{-121-3\sqrt{561}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+3\sqrt{561}}{2*11}=\frac{-121+3\sqrt{561}}{22} $
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