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8/7x+1-1/5x=101/35
We move all terms to the left:
8/7x+1-1/5x-(101/35)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
8/7x-1/5x+1-(+101/35)=0
We get rid of parentheses
8/7x-1/5x+1-101/35=0
We calculate fractions
(-17675x^2)/3675x^2+4200x/3675x^2+(-735x)/3675x^2+1=0
We multiply all the terms by the denominator
(-17675x^2)+4200x+(-735x)+1*3675x^2=0
Wy multiply elements
(-17675x^2)+3675x^2+4200x+(-735x)=0
We get rid of parentheses
-17675x^2+3675x^2+4200x-735x=0
We add all the numbers together, and all the variables
-14000x^2+3465x=0
a = -14000; b = 3465; c = 0;
Δ = b2-4ac
Δ = 34652-4·(-14000)·0
Δ = 12006225
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{12006225}=3465$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3465)-3465}{2*-14000}=\frac{-6930}{-28000} =99/400 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3465)+3465}{2*-14000}=\frac{0}{-28000} =0 $
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