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5a^2-9a-1=0
a = 5; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·5·(-1)
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{101}}{2*5}=\frac{9-\sqrt{101}}{10} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{101}}{2*5}=\frac{9+\sqrt{101}}{10} $
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