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X=2000/(3X)
We move all terms to the left:
X-(2000/(3X))=0
Domain of the equation: 3X)!=0We add all the numbers together, and all the variables
X!=0/1
X!=0
X∈R
X-(+2000/3X)=0
We get rid of parentheses
X-2000/3X=0
We multiply all the terms by the denominator
X*3X-2000=0
Wy multiply elements
3X^2-2000=0
a = 3; b = 0; c = -2000;
Δ = b2-4ac
Δ = 02-4·3·(-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{-(0)-40\sqrt{15}}{2*3}=\frac{0-40\sqrt{15}}{6} =-\frac{40\sqrt{15}}{6} =-\frac{20\sqrt{15}}{3} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{15}}{2*3}=\frac{0+40\sqrt{15}}{6} =\frac{40\sqrt{15}}{6} =\frac{20\sqrt{15}}{3} $
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