7/9b+1/3b=1/10

Solution for 7/9b+1/3b=1/10 equation:

7/9b+1/3b=1/10

We move all terms to the left:

7/9b+1/3b-(1/10)=0


Domain of the equation: 9b!=0

b!=0/9

b!=0

b∈R



Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

7/9b+1/3b-(+1/10)=0

We get rid of parentheses

7/9b+1/3b-1/10=0

We calculate fractions


(-81b^2)/270b^2+210b/270b^2+90b/270b^2=0

We multiply all the terms by the denominator


(-81b^2)+210b+90b=0

We add all the numbers together, and all the variables

(-81b^2)+300b=0

We get rid of parentheses

-81b^2+300b=0

a = -81; b = 300; c = 0;
Δ = b2-4ac
Δ = 3002-4·(-81)·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-300}{2*-81}=\frac{-600}{-162}
=3+19/27
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+300}{2*-81}=\frac{0}{-162}
=0
$