x^2+500*x+20000=0

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Solution for x^2+500*x+20000=0 equation:



x^2+500x+20000=0
a = 1; b = 500; c = +20000;
Δ = b2-4ac
Δ = 5002-4·1·20000
Δ = 170000
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:
$\sqrt{\Delta}=\sqrt{170000}=\sqrt{10000*17}=\sqrt{10000}*\sqrt{17}=100\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-100\sqrt{17}}{2*1}=\frac{-500-100\sqrt{17}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+100\sqrt{17}}{2*1}=\frac{-500+100\sqrt{17}}{2} $

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