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9x^2-108x-172=0
a = 9; b = -108; c = -172;
Δ = b2-4ac
Δ = -1082-4·9·(-172)
Δ = 17856
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17856}=\sqrt{576*31}=\sqrt{576}*\sqrt{31}=24\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-24\sqrt{31}}{2*9}=\frac{108-24\sqrt{31}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+24\sqrt{31}}{2*9}=\frac{108+24\sqrt{31}}{18} $
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