5/5b+6=2/b-2

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Solution for 5/5b+6=2/b-2 equation:



5/5b+6=2/b-2
We move all terms to the left:
5/5b+6-(2/b-2)=0
Domain of the equation: 5b!=0
b!=0/5
b!=0
b∈R
Domain of the equation: b-2)!=0
b∈R
We get rid of parentheses
5/5b-2/b+2+6=0
We calculate fractions
5b/5b^2+(-10b)/5b^2+2+6=0
We add all the numbers together, and all the variables
5b/5b^2+(-10b)/5b^2+8=0
We multiply all the terms by the denominator
5b+(-10b)+8*5b^2=0
Wy multiply elements
40b^2+5b+(-10b)=0
We get rid of parentheses
40b^2+5b-10b=0
We add all the numbers together, and all the variables
40b^2-5b=0
a = 40; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·40·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*40}=\frac{0}{80} =0 $
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*40}=\frac{10}{80} =1/8 $

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