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9x^2-71x+102=0
a = 9; b = -71; c = +102;
Δ = b2-4ac
Δ = -712-4·9·102
Δ = 1369
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{1369}=37$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-37}{2*9}=\frac{34}{18} =1+8/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+37}{2*9}=\frac{108}{18} =6 $
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