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6x^2-43x+77=0
a = 6; b = -43; c = +77;
Δ = b2-4ac
Δ = -432-4·6·77
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-1}{2*6}=\frac{42}{12} =3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+1}{2*6}=\frac{44}{12} =3+2/3 $
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