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x^2-60x-600=0
a = 1; b = -60; c = -600;
Δ = b2-4ac
Δ = -602-4·1·(-600)
Δ = 6000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{15}}{2*1}=\frac{60-20\sqrt{15}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{15}}{2*1}=\frac{60+20\sqrt{15}}{2} $
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