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

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

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

We move all terms to the left:

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


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 4b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


16b/12b^2+3b/12b^2-4+2=0

We add all the numbers together, and all the variables

16b/12b^2+3b/12b^2-2=0

We multiply all the terms by the denominator


16b+3b-2*12b^2=0

We add all the numbers together, and all the variables

19b-2*12b^2=0

Wy multiply elements

-24b^2+19b=0

a = -24; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-24)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-24}=\frac{-38}{-48}
=19/24
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-24}=\frac{0}{-48}
=0
$