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6/7x+4=3/5x-3
We move all terms to the left:
6/7x+4-(3/5x-3)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 5x-3)!=0We get rid of parentheses
x∈R
6/7x-3/5x+3+4=0
We calculate fractions
30x/35x^2+(-21x)/35x^2+3+4=0
We add all the numbers together, and all the variables
30x/35x^2+(-21x)/35x^2+7=0
We multiply all the terms by the denominator
30x+(-21x)+7*35x^2=0
Wy multiply elements
245x^2+30x+(-21x)=0
We get rid of parentheses
245x^2+30x-21x=0
We add all the numbers together, and all the variables
245x^2+9x=0
a = 245; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·245·0
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*245}=\frac{-18}{490} =-9/245 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*245}=\frac{0}{490} =0 $
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