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5a^2-17a+11=0
a = 5; b = -17; c = +11;
Δ = b2-4ac
Δ = -172-4·5·11
Δ = 69
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{-(-17)-\sqrt{69}}{2*5}=\frac{17-\sqrt{69}}{10} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{69}}{2*5}=\frac{17+\sqrt{69}}{10} $
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