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6x^2+47x-34=0
a = 6; b = 47; c = -34;
Δ = b2-4ac
Δ = 472-4·6·(-34)
Δ = 3025
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{3025}=55$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-55}{2*6}=\frac{-102}{12} =-8+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+55}{2*6}=\frac{8}{12} =2/3 $
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