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40=0.0036x-0.35x^2+8.5x
We move all terms to the left:
40-(0.0036x-0.35x^2+8.5x)=0
We get rid of parentheses
0.35x^2-0.0036x-8.5x+40=0
We add all the numbers together, and all the variables
0.35x^2-8.5036x+40=0
a = 0.35; b = -8.5036; c = +40;
Δ = b2-4ac
Δ = -8.50362-4·0.35·40
Δ = 16.31121296
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8.5036)-\sqrt{16.31121296}}{2*0.35}=\frac{8.5036-\sqrt{16.31121296}}{0.7} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.5036)+\sqrt{16.31121296}}{2*0.35}=\frac{8.5036+\sqrt{16.31121296}}{0.7} $
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