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85x-0.5x^2-45x+300=50
We move all terms to the left:
85x-0.5x^2-45x+300-(50)=0
We add all the numbers together, and all the variables
-0.5x^2+40x+250=0
a = -0.5; b = 40; c = +250;
Δ = b2-4ac
Δ = 402-4·(-0.5)·250
Δ = 2100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{21}}{2*-0.5}=\frac{-40-10\sqrt{21}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{21}}{2*-0.5}=\frac{-40+10\sqrt{21}}{-1} $
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