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6y^2-55y+9=0
a = 6; b = -55; c = +9;
Δ = b2-4ac
Δ = -552-4·6·9
Δ = 2809
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{2809}=53$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-53}{2*6}=\frac{2}{12} =1/6 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+53}{2*6}=\frac{108}{12} =9 $
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