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x^2+19x-2000=0
a = 1; b = 19; c = -2000;
Δ = b2-4ac
Δ = 192-4·1·(-2000)
Δ = 8361
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8361}=\sqrt{9*929}=\sqrt{9}*\sqrt{929}=3\sqrt{929}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3\sqrt{929}}{2*1}=\frac{-19-3\sqrt{929}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3\sqrt{929}}{2*1}=\frac{-19+3\sqrt{929}}{2} $
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