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3x^2-43x+14=0
a = 3; b = -43; c = +14;
Δ = b2-4ac
Δ = -432-4·3·14
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-41}{2*3}=\frac{2}{6} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+41}{2*3}=\frac{84}{6} =14 $
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