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9x^2-47x+42=0
a = 9; b = -47; c = +42;
Δ = b2-4ac
Δ = -472-4·9·42
Δ = 697
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{697}}{2*9}=\frac{47-\sqrt{697}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{697}}{2*9}=\frac{47+\sqrt{697}}{18} $
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