3+4/3b=7/15b

Solution for 3+4/3b=7/15b equation:

3+4/3b=7/15b

We move all terms to the left:

3+4/3b-(7/15b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 15b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

4/3b-(+7/15b)+3=0

We get rid of parentheses

4/3b-7/15b+3=0

We calculate fractions


60b/45b^2+(-21b)/45b^2+3=0

We multiply all the terms by the denominator


60b+(-21b)+3*45b^2=0

Wy multiply elements

135b^2+60b+(-21b)=0

We get rid of parentheses

135b^2+60b-21b=0

We add all the numbers together, and all the variables

135b^2+39b=0

a = 135; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·135·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*135}=\frac{-78}{270}
=-13/45
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*135}=\frac{0}{270}
=0
$