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x^2-800x-4600=0
a = 1; b = -800; c = -4600;
Δ = b2-4ac
Δ = -8002-4·1·(-4600)
Δ = 658400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{658400}=\sqrt{400*1646}=\sqrt{400}*\sqrt{1646}=20\sqrt{1646}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-20\sqrt{1646}}{2*1}=\frac{800-20\sqrt{1646}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+20\sqrt{1646}}{2*1}=\frac{800+20\sqrt{1646}}{2} $
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