5/3b-5=3/2b+12

Solution for 5/3b-5=3/2b+12 equation:

5/3b-5=3/2b+12

We move all terms to the left:

5/3b-5-(3/2b+12)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 2b+12)!=0

b∈R


We get rid of parentheses

5/3b-3/2b-12-5=0

We calculate fractions


10b/6b^2+(-9b)/6b^2-12-5=0

We add all the numbers together, and all the variables

10b/6b^2+(-9b)/6b^2-17=0

We multiply all the terms by the denominator


10b+(-9b)-17*6b^2=0

Wy multiply elements

-102b^2+10b+(-9b)=0

We get rid of parentheses

-102b^2+10b-9b=0

We add all the numbers together, and all the variables

-102b^2+b=0

a = -102; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-102)·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*-102}=\frac{-2}{-204}
=1/102
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-102}=\frac{0}{-204}
=0
$