4/5+1/5b=4-1/3b

Solution for 4/5+1/5b=4-1/3b equation:

4/5+1/5b=4-1/3b

We move all terms to the left:

4/5+1/5b-(4-1/3b)=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

1/5b-(-1/3b+4)+4/5=0

We get rid of parentheses

1/5b+1/3b-4+4/5=0

We calculate fractions


3b/375b^2+125b/375b^2+12b/375b^2-4=0

We multiply all the terms by the denominator


3b+125b+12b-4*375b^2=0

We add all the numbers together, and all the variables

140b-4*375b^2=0

Wy multiply elements

-1500b^2+140b=0

a = -1500; b = 140; c = 0;
Δ = b2-4ac
Δ = 1402-4·(-1500)·0
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-140}{2*-1500}=\frac{-280}{-3000}
=7/75
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+140}{2*-1500}=\frac{0}{-3000}
=0
$