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x(250-x)=6.5
We move all terms to the left:
x(250-x)-(6.5)=0
We add all the numbers together, and all the variables
x(-1x+250)-(6.5)=0
We add all the numbers together, and all the variables
x(-1x+250)-6.5=0
We multiply parentheses
-1x^2+250x-6.5=0
a = -1; b = 250; c = -6.5;
Δ = b2-4ac
Δ = 2502-4·(-1)·(-6.5)
Δ = 62474
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-\sqrt{62474}}{2*-1}=\frac{-250-\sqrt{62474}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+\sqrt{62474}}{2*-1}=\frac{-250+\sqrt{62474}}{-2} $
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