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6y^2+35y+46=0
a = 6; b = 35; c = +46;
Δ = b2-4ac
Δ = 352-4·6·46
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{121}=11$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-11}{2*6}=\frac{-46}{12} =-3+5/6 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+11}{2*6}=\frac{-24}{12} =-2 $
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