5/5b+3=2/b-3

Solution for 5/5b+3=2/b-3 equation:

5/5b+3=2/b-3

We move all terms to the left:

5/5b+3-(2/b-3)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: b-3)!=0

b∈R


We get rid of parentheses

5/5b-2/b+3+3=0

We calculate fractions


5b/5b^2+(-10b)/5b^2+3+3=0

We add all the numbers together, and all the variables

5b/5b^2+(-10b)/5b^2+6=0

We multiply all the terms by the denominator


5b+(-10b)+6*5b^2=0

Wy multiply elements

30b^2+5b+(-10b)=0

We get rid of parentheses

30b^2+5b-10b=0

We add all the numbers together, and all the variables

30b^2-5b=0

a = 30; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·30·0
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*30}=\frac{0}{60}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*30}=\frac{10}{60}
=1/6
$