3+(4)/(9)b=-(2)/(3)b

Solution for 3+(4)/(9)b=-(2)/(3)b equation:

3+(4)/(9)b=-(2)/(3)b

We move all terms to the left:

3+(4)/(9)b-(-(2)/(3)b)=0


Domain of the equation: 9b!=0

b!=0/9

b!=0

b∈R



Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We get rid of parentheses

4/9b+2/3b+3=0

We calculate fractions


12b/27b^2+18b/27b^2+3=0

We multiply all the terms by the denominator


12b+18b+3*27b^2=0

We add all the numbers together, and all the variables

30b+3*27b^2=0

Wy multiply elements

81b^2+30b=0

a = 81; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·81·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*81}=\frac{-60}{162}
=-10/27
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*81}=\frac{0}{162}
=0
$