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x^2+600x+17500=0
a = 1; b = 600; c = +17500;
Δ = b2-4ac
Δ = 6002-4·1·17500
Δ = 290000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{290000}=\sqrt{10000*29}=\sqrt{10000}*\sqrt{29}=100\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-100\sqrt{29}}{2*1}=\frac{-600-100\sqrt{29}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+100\sqrt{29}}{2*1}=\frac{-600+100\sqrt{29}}{2} $
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