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200=86x-0.4x^2
We move all terms to the left:
200-(86x-0.4x^2)=0
We get rid of parentheses
0.4x^2-86x+200=0
a = 0.4; b = -86; c = +200;
Δ = b2-4ac
Δ = -862-4·0.4·200
Δ = 7076
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7076}=\sqrt{4*1769}=\sqrt{4}*\sqrt{1769}=2\sqrt{1769}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{1769}}{2*0.4}=\frac{86-2\sqrt{1769}}{0.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{1769}}{2*0.4}=\frac{86+2\sqrt{1769}}{0.8} $
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