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X2-1000X-300000=0
We add all the numbers together, and all the variables
X^2-1000X-300000=0
a = 1; b = -1000; c = -300000;
Δ = b2-4ac
Δ = -10002-4·1·(-300000)
Δ = 2200000
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2200000}=\sqrt{40000*55}=\sqrt{40000}*\sqrt{55}=200\sqrt{55}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-200\sqrt{55}}{2*1}=\frac{1000-200\sqrt{55}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+200\sqrt{55}}{2*1}=\frac{1000+200\sqrt{55}}{2} $
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