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50x^2-110x-240=0
a = 50; b = -110; c = -240;
Δ = b2-4ac
Δ = -1102-4·50·(-240)
Δ = 60100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60100}=\sqrt{100*601}=\sqrt{100}*\sqrt{601}=10\sqrt{601}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-10\sqrt{601}}{2*50}=\frac{110-10\sqrt{601}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+10\sqrt{601}}{2*50}=\frac{110+10\sqrt{601}}{100} $
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