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6x^2-77x+240=0
a = 6; b = -77; c = +240;
Δ = b2-4ac
Δ = -772-4·6·240
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-13}{2*6}=\frac{64}{12} =5+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+13}{2*6}=\frac{90}{12} =7+1/2 $
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