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(C)=2000+50C-0.5C^2
We move all terms to the left:
(C)-(2000+50C-0.5C^2)=0
We get rid of parentheses
0.5C^2-50C+C-2000=0
We add all the numbers together, and all the variables
0.5C^2-49C-2000=0
a = 0.5; b = -49; c = -2000;
Δ = b2-4ac
Δ = -492-4·0.5·(-2000)
Δ = 6401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{6401}}{2*0.5}=\frac{49-\sqrt{6401}}{1} $$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{6401}}{2*0.5}=\frac{49+\sqrt{6401}}{1} $
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