3/4b-2/3b=-9

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

3/4b-2/3b=-9

We move all terms to the left:

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


Domain of the equation: 4b!=0

b!=0/4

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

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

We calculate fractions


9b/12b^2+(-8b)/12b^2+9=0

We multiply all the terms by the denominator


9b+(-8b)+9*12b^2=0

Wy multiply elements

108b^2+9b+(-8b)=0

We get rid of parentheses

108b^2+9b-8b=0

We add all the numbers together, and all the variables

108b^2+b=0

a = 108; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·108·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*108}=\frac{-2}{216}
=-1/108
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*108}=\frac{0}{216}
=0
$