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19x^2+5x-100=0
a = 19; b = 5; c = -100;
Δ = b2-4ac
Δ = 52-4·19·(-100)
Δ = 7625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7625}=\sqrt{25*305}=\sqrt{25}*\sqrt{305}=5\sqrt{305}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{305}}{2*19}=\frac{-5-5\sqrt{305}}{38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{305}}{2*19}=\frac{-5+5\sqrt{305}}{38} $
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