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

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

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

We move all terms to the left:

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


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-48b^2)/300b^2+100b/300b^2+75b/300b^2=0

We multiply all the terms by the denominator


(-48b^2)+100b+75b=0

We add all the numbers together, and all the variables

(-48b^2)+175b=0

We get rid of parentheses

-48b^2+175b=0

a = -48; b = 175; c = 0;
Δ = b2-4ac
Δ = 1752-4·(-48)·0
Δ = 30625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30625}=175$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(175)-175}{2*-48}=\frac{-350}{-96}
=3+31/48
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(175)+175}{2*-48}=\frac{0}{-96}
=0
$