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6x^2-47x-6=0
a = 6; b = -47; c = -6;
Δ = b2-4ac
Δ = -472-4·6·(-6)
Δ = 2353
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{2353}}{2*6}=\frac{47-\sqrt{2353}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2353}}{2*6}=\frac{47+\sqrt{2353}}{12} $
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