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6x^2-71x-120=0
a = 6; b = -71; c = -120;
Δ = b2-4ac
Δ = -712-4·6·(-120)
Δ = 7921
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{7921}=89$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-89}{2*6}=\frac{-18}{12} =-1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+89}{2*6}=\frac{160}{12} =13+1/3 $
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