-4+2/3b=1/2b-5

Solution for -4+2/3b=1/2b-5 equation:

-4+2/3b=1/2b-5

We move all terms to the left:

-4+2/3b-(1/2b-5)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 2b-5)!=0

b∈R


We get rid of parentheses

2/3b-1/2b+5-4=0

We calculate fractions


4b/6b^2+(-3b)/6b^2+5-4=0

We add all the numbers together, and all the variables

4b/6b^2+(-3b)/6b^2+1=0

We multiply all the terms by the denominator


4b+(-3b)+1*6b^2=0

Wy multiply elements

6b^2+4b+(-3b)=0

We get rid of parentheses

6b^2+4b-3b=0

We add all the numbers together, and all the variables

6b^2+b=0

a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
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*6}=\frac{-2}{12}
=-1/6
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*6}=\frac{0}{12}
=0
$