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11/7x+49-2/x+7=5/7
We move all terms to the left:
11/7x+49-2/x+7-(5/7)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
11/7x-2/x+49+7-(+5/7)=0
We add all the numbers together, and all the variables
11/7x-2/x+56-(+5/7)=0
We get rid of parentheses
11/7x-2/x+56-5/7=0
We calculate fractions
11x/343x^2+(-686x)/343x^2+(-5x)/343x^2+56=0
We multiply all the terms by the denominator
11x+(-686x)+(-5x)+56*343x^2=0
Wy multiply elements
19208x^2+11x+(-686x)+(-5x)=0
We get rid of parentheses
19208x^2+11x-686x-5x=0
We add all the numbers together, and all the variables
19208x^2-680x=0
a = 19208; b = -680; c = 0;
Δ = b2-4ac
Δ = -6802-4·19208·0
Δ = 462400
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{462400}=680$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-680)-680}{2*19208}=\frac{0}{38416} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-680)+680}{2*19208}=\frac{1360}{38416} =85/2401 $
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