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33x^2+42x-110.25=0
a = 33; b = 42; c = -110.25;
Δ = b2-4ac
Δ = 422-4·33·(-110.25)
Δ = 16317
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16317}=\sqrt{441*37}=\sqrt{441}*\sqrt{37}=21\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-21\sqrt{37}}{2*33}=\frac{-42-21\sqrt{37}}{66} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+21\sqrt{37}}{2*33}=\frac{-42+21\sqrt{37}}{66} $
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