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9x^2-53x+40=0
a = 9; b = -53; c = +40;
Δ = b2-4ac
Δ = -532-4·9·40
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-37}{2*9}=\frac{16}{18} =8/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+37}{2*9}=\frac{90}{18} =5 $
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