3/2b-7/3b=5/6

Solution for 3/2b-7/3b=5/6 equation:

3/2b-7/3b=5/6

We move all terms to the left:

3/2b-7/3b-(5/6)=0


Domain of the equation: 2b!=0

b!=0/2

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

3/2b-7/3b-(+5/6)=0

We get rid of parentheses

3/2b-7/3b-5/6=0

We calculate fractions


(-90b^2)/216b^2+324b/216b^2+(-504b)/216b^2=0

We multiply all the terms by the denominator


(-90b^2)+324b+(-504b)=0

We get rid of parentheses

-90b^2+324b-504b=0

We add all the numbers together, and all the variables

-90b^2-180b=0

a = -90; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·(-90)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*-90}=\frac{0}{-180}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*-90}=\frac{360}{-180}
=-2
$