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5/5x+7=1/8x
We move all terms to the left:
5/5x+7-(1/8x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 8x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/5x-(+1/8x)+7=0
We get rid of parentheses
5/5x-1/8x+7=0
We calculate fractions
40x/40x^2+(-5x)/40x^2+7=0
We multiply all the terms by the denominator
40x+(-5x)+7*40x^2=0
Wy multiply elements
280x^2+40x+(-5x)=0
We get rid of parentheses
280x^2+40x-5x=0
We add all the numbers together, and all the variables
280x^2+35x=0
a = 280; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·280·0
Δ = 1225
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{1225}=35$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*280}=\frac{-70}{560} =-1/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*280}=\frac{0}{560} =0 $
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