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200=-1000x^2+1100x-25
We move all terms to the left:
200-(-1000x^2+1100x-25)=0
We get rid of parentheses
1000x^2-1100x+25+200=0
We add all the numbers together, and all the variables
1000x^2-1100x+225=0
a = 1000; b = -1100; c = +225;
Δ = b2-4ac
Δ = -11002-4·1000·225
Δ = 310000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{310000}=\sqrt{10000*31}=\sqrt{10000}*\sqrt{31}=100\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1100)-100\sqrt{31}}{2*1000}=\frac{1100-100\sqrt{31}}{2000} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1100)+100\sqrt{31}}{2*1000}=\frac{1100+100\sqrt{31}}{2000} $
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