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9x^2-12x-125=0
a = 9; b = -12; c = -125;
Δ = b2-4ac
Δ = -122-4·9·(-125)
Δ = 4644
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4644}=\sqrt{36*129}=\sqrt{36}*\sqrt{129}=6\sqrt{129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{129}}{2*9}=\frac{12-6\sqrt{129}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{129}}{2*9}=\frac{12+6\sqrt{129}}{18} $
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