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50x+x^2/100+200=27700
We move all terms to the left:
50x+x^2/100+200-(27700)=0
We add all the numbers together, and all the variables
x^2/100+50x-27500=0
We multiply all the terms by the denominator
x^2+50x*100-27500*100=0
We add all the numbers together, and all the variables
x^2+50x*100-2750000=0
Wy multiply elements
x^2+5000x-2750000=0
a = 1; b = 5000; c = -2750000;
Δ = b2-4ac
Δ = 50002-4·1·(-2750000)
Δ = 36000000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{36000000}=6000$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-6000}{2*1}=\frac{-11000}{2} =-5500 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+6000}{2*1}=\frac{1000}{2} =500 $
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