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3x^2-47x+71=0
a = 3; b = -47; c = +71;
Δ = b2-4ac
Δ = -472-4·3·71
Δ = 1357
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{1357}}{2*3}=\frac{47-\sqrt{1357}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{1357}}{2*3}=\frac{47+\sqrt{1357}}{6} $
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