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5x^2+10000x-100000=0
a = 5; b = 10000; c = -100000;
Δ = b2-4ac
Δ = 100002-4·5·(-100000)
Δ = 102000000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102000000}=\sqrt{1000000*102}=\sqrt{1000000}*\sqrt{102}=1000\sqrt{102}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10000)-1000\sqrt{102}}{2*5}=\frac{-10000-1000\sqrt{102}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10000)+1000\sqrt{102}}{2*5}=\frac{-10000+1000\sqrt{102}}{10} $
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