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1/2x+2/3x+5/3x=3/5
We move all terms to the left:
1/2x+2/3x+5/3x-(3/5)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
1/2x+2/3x+5/3x-(+3/5)=0
We get rid of parentheses
1/2x+2/3x+5/3x-3/5=0
We calculate fractions
(-54x^2)/150x^2+75x/150x^2+(250x+2)/150x^2=0
We multiply all the terms by the denominator
(-54x^2)+75x+(250x+2)=0
We get rid of parentheses
-54x^2+75x+250x+2=0
We add all the numbers together, and all the variables
-54x^2+325x+2=0
a = -54; b = 325; c = +2;
Δ = b2-4ac
Δ = 3252-4·(-54)·2
Δ = 106057
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{-(325)-\sqrt{106057}}{2*-54}=\frac{-325-\sqrt{106057}}{-108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(325)+\sqrt{106057}}{2*-54}=\frac{-325+\sqrt{106057}}{-108} $
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