-1/3b-8=-3+1/2b

Solution for -1/3b-8=-3+1/2b equation:

-1/3b-8=-3+1/2b

We move all terms to the left:

-1/3b-8-(-3+1/2b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 2b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-1/3b-(1/2b-3)-8=0

We get rid of parentheses

-1/3b-1/2b+3-8=0

We calculate fractions


(-2b)/6b^2+(-3b)/6b^2+3-8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-2b)+(-3b)-5*6b^2=0

Wy multiply elements

-30b^2+(-2b)+(-3b)=0

We get rid of parentheses

-30b^2-2b-3b=0

We add all the numbers together, and all the variables

-30b^2-5b=0

a = -30; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-30)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-30}=\frac{0}{-60}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-30}=\frac{10}{-60}
=-1/6
$