4/5b+2/15=8/3b

Solution for 4/5b+2/15=8/3b equation:

4/5b+2/15=8/3b

We move all terms to the left:

4/5b+2/15-(8/3b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

4/5b-(+8/3b)+2/15=0

We get rid of parentheses

4/5b-8/3b+2/15=0

We calculate fractions


90b^2/225b^2+180b/225b^2+(-600b)/225b^2=0

We multiply all the terms by the denominator


90b^2+180b+(-600b)=0

We get rid of parentheses

90b^2+180b-600b=0

We add all the numbers together, and all the variables

90b^2-420b=0

a = 90; b = -420; c = 0;
Δ = b2-4ac
Δ = -4202-4·90·0
Δ = 176400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{176400}=420$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-420}{2*90}=\frac{0}{180}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+420}{2*90}=\frac{840}{180}
=4+2/3
$