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0=-5x^2+550x+5000
We move all terms to the left:
0-(-5x^2+550x+5000)=0
We add all the numbers together, and all the variables
-(-5x^2+550x+5000)=0
We get rid of parentheses
5x^2-550x-5000=0
a = 5; b = -550; c = -5000;
Δ = b2-4ac
Δ = -5502-4·5·(-5000)
Δ = 402500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{402500}=\sqrt{2500*161}=\sqrt{2500}*\sqrt{161}=50\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-550)-50\sqrt{161}}{2*5}=\frac{550-50\sqrt{161}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-550)+50\sqrt{161}}{2*5}=\frac{550+50\sqrt{161}}{10} $
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