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9x^2-57x+72=0
a = 9; b = -57; c = +72;
Δ = b2-4ac
Δ = -572-4·9·72
Δ = 657
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{73}}{2*9}=\frac{57-3\sqrt{73}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{73}}{2*9}=\frac{57+3\sqrt{73}}{18} $
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