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5x^2+17x-109=0
a = 5; b = 17; c = -109;
Δ = b2-4ac
Δ = 172-4·5·(-109)
Δ = 2469
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{2469}}{2*5}=\frac{-17-\sqrt{2469}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{2469}}{2*5}=\frac{-17+\sqrt{2469}}{10} $
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