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-9x^2+109x-252=0
a = -9; b = 109; c = -252;
Δ = b2-4ac
Δ = 1092-4·(-9)·(-252)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(109)-53}{2*-9}=\frac{-162}{-18} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(109)+53}{2*-9}=\frac{-56}{-18} =3+1/9 $
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