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x+2/2x=x+9/3x+5
We move all terms to the left:
x+2/2x-(x+9/3x+5)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x+5)!=0We get rid of parentheses
x∈R
x+2/2x-x-9/3x-5=0
We calculate fractions
x-x+6x/6x^2+(-18x)/6x^2-5=0
We add all the numbers together, and all the variables
6x/6x^2+(-18x)/6x^2-5=0
We multiply all the terms by the denominator
6x+(-18x)-5*6x^2=0
Wy multiply elements
-30x^2+6x+(-18x)=0
We get rid of parentheses
-30x^2+6x-18x=0
We add all the numbers together, and all the variables
-30x^2-12x=0
a = -30; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-30)·0
Δ = 144
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{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-30}=\frac{0}{-60} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-30}=\frac{24}{-60} =-2/5 $
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