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90=250x-0.5x^2
We move all terms to the left:
90-(250x-0.5x^2)=0
We get rid of parentheses
0.5x^2-250x+90=0
a = 0.5; b = -250; c = +90;
Δ = b2-4ac
Δ = -2502-4·0.5·90
Δ = 62320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{62320}=\sqrt{16*3895}=\sqrt{16}*\sqrt{3895}=4\sqrt{3895}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-4\sqrt{3895}}{2*0.5}=\frac{250-4\sqrt{3895}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+4\sqrt{3895}}{2*0.5}=\frac{250+4\sqrt{3895}}{1} $
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