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5/3x-4/5=2/7x
We move all terms to the left:
5/3x-4/5-(2/7x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 7x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/3x-(+2/7x)-4/5=0
We get rid of parentheses
5/3x-2/7x-4/5=0
We calculate fractions
(-588x^2)/525x^2+875x/525x^2+(-150x)/525x^2=0
We multiply all the terms by the denominator
(-588x^2)+875x+(-150x)=0
We get rid of parentheses
-588x^2+875x-150x=0
We add all the numbers together, and all the variables
-588x^2+725x=0
a = -588; b = 725; c = 0;
Δ = b2-4ac
Δ = 7252-4·(-588)·0
Δ = 525625
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{525625}=725$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(725)-725}{2*-588}=\frac{-1450}{-1176} =1+137/588 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(725)+725}{2*-588}=\frac{0}{-1176} =0 $
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