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85x-0.5x^2-45x+300=
We move all terms to the left:
85x-0.5x^2-45x+300-()=0
We add all the numbers together, and all the variables
-0.5x^2+40x=0
a = -0.5; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-0.5)·0
Δ = 1600
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{1600}=40$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-0.5}=\frac{-80}{-1} =+80 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-0.5}=\frac{0}{-1} =0 $
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