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500x+-2x^2=300x+2000
We move all terms to the left:
500x+-2x^2-(300x+2000)=0
We add all the numbers together, and all the variables
-2x^2+500x-(300x+2000)=0
We get rid of parentheses
-2x^2+500x-300x-2000=0
We add all the numbers together, and all the variables
-2x^2+200x-2000=0
a = -2; b = 200; c = -2000;
Δ = b2-4ac
Δ = 2002-4·(-2)·(-2000)
Δ = 24000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24000}=\sqrt{1600*15}=\sqrt{1600}*\sqrt{15}=40\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-40\sqrt{15}}{2*-2}=\frac{-200-40\sqrt{15}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+40\sqrt{15}}{2*-2}=\frac{-200+40\sqrt{15}}{-4} $
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