1/5b+5=1/2b-1

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Solution for 1/5b+5=1/2b-1 equation:



1/5b+5=1/2b-1
We move all terms to the left:
1/5b+5-(1/2b-1)=0
Domain of the equation: 5b!=0
b!=0/5
b!=0
b∈R
Domain of the equation: 2b-1)!=0
b∈R
We get rid of parentheses
1/5b-1/2b+1+5=0
We calculate fractions
2b/10b^2+(-5b)/10b^2+1+5=0
We add all the numbers together, and all the variables
2b/10b^2+(-5b)/10b^2+6=0
We multiply all the terms by the denominator
2b+(-5b)+6*10b^2=0
Wy multiply elements
60b^2+2b+(-5b)=0
We get rid of parentheses
60b^2+2b-5b=0
We add all the numbers together, and all the variables
60b^2-3b=0
a = 60; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·60·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*60}=\frac{0}{120} =0 $
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*60}=\frac{6}{120} =1/20 $

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