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3x+5=2/x
We move all terms to the left:
3x+5-(2/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3x-(+2/x)+5=0
We get rid of parentheses
3x-2/x+5=0
We multiply all the terms by the denominator
3x*x+5*x-2=0
We add all the numbers together, and all the variables
5x+3x*x-2=0
Wy multiply elements
3x^2+5x-2=0
a = 3; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·3·(-2)
Δ = 49
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*3}=\frac{-12}{6} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*3}=\frac{2}{6} =1/3 $
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