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3/8+5/7x=7/9x
We move all terms to the left:
3/8+5/7x-(7/9x)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 9x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/7x-(+7/9x)+3/8=0
We get rid of parentheses
5/7x-7/9x+3/8=0
We calculate fractions
1701x^2/4032x^2+2880x/4032x^2+(-3136x)/4032x^2=0
We multiply all the terms by the denominator
1701x^2+2880x+(-3136x)=0
We get rid of parentheses
1701x^2+2880x-3136x=0
We add all the numbers together, and all the variables
1701x^2-256x=0
a = 1701; b = -256; c = 0;
Δ = b2-4ac
Δ = -2562-4·1701·0
Δ = 65536
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{65536}=256$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-256}{2*1701}=\frac{0}{3402} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+256}{2*1701}=\frac{512}{3402} =256/1701 $
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