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

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

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

We move all terms to the left:

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


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-60b^2)/216b^2+504b/216b^2+(-324b)/216b^2=0

We multiply all the terms by the denominator


(-60b^2)+504b+(-324b)=0

We get rid of parentheses

-60b^2+504b-324b=0

We add all the numbers together, and all the variables

-60b^2+180b=0

a = -60; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-60)·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*-60}=\frac{-360}{-120}
=+3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-60}=\frac{0}{-120}
=0
$