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

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
$