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6x^2-43x+7=0
a = 6; b = -43; c = +7;
Δ = b2-4ac
Δ = -432-4·6·7
Δ = 1681
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{1681}=41$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-41}{2*6}=\frac{2}{12} =1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+41}{2*6}=\frac{84}{12} =7 $
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