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19x^2+5x-1=0
a = 19; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·19·(-1)
Δ = 101
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{-(5)-\sqrt{101}}{2*19}=\frac{-5-\sqrt{101}}{38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{101}}{2*19}=\frac{-5+\sqrt{101}}{38} $
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