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0=110x-(3100+6x+0.1x^2)
We move all terms to the left:
0-(110x-(3100+6x+0.1x^2))=0
We add all the numbers together, and all the variables
-(110x-(3100+6x+0.1x^2))=0
We calculate terms in parentheses: -(110x-(3100+6x+0.1x^2)), so:We get rid of parentheses
110x-(3100+6x+0.1x^2)
determiningTheFunctionDomain -(3100+6x+0.1x^2)+110x
We get rid of parentheses
-0.1x^2-6x+110x-3100
We add all the numbers together, and all the variables
-0.1x^2+104x-3100
Back to the equation:
-(-0.1x^2+104x-3100)
0.1x^2-104x+3100=0
a = 0.1; b = -104; c = +3100;
Δ = b2-4ac
Δ = -1042-4·0.1·3100
Δ = 9576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9576}=\sqrt{36*266}=\sqrt{36}*\sqrt{266}=6\sqrt{266}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-6\sqrt{266}}{2*0.1}=\frac{104-6\sqrt{266}}{0.2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+6\sqrt{266}}{2*0.1}=\frac{104+6\sqrt{266}}{0.2} $
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