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84000+60x=200x-0.03125x^2
We move all terms to the left:
84000+60x-(200x-0.03125x^2)=0
We get rid of parentheses
0.03125x^2-200x+60x+84000=0
We add all the numbers together, and all the variables
0.03125x^2-140x+84000=0
a = 0.03125; b = -140; c = +84000;
Δ = b2-4ac
Δ = -1402-4·0.03125·84000
Δ = 9100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9100}=\sqrt{100*91}=\sqrt{100}*\sqrt{91}=10\sqrt{91}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-10\sqrt{91}}{2*0.03125}=\frac{140-10\sqrt{91}}{0.0625} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+10\sqrt{91}}{2*0.03125}=\frac{140+10\sqrt{91}}{0.0625} $
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