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-6x^2+55x-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:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2809}=53$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-53}{2*-6}=\frac{-108}{-12} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+53}{2*-6}=\frac{-2}{-12} =1/6 $
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