-1/4b+6=2/3b+28

Solution for -1/4b+6=2/3b+28 equation:

-1/4b+6=2/3b+28

We move all terms to the left:

-1/4b+6-(2/3b+28)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 3b+28)!=0

b∈R


We get rid of parentheses

-1/4b-2/3b-28+6=0

We calculate fractions


(-3b)/12b^2+(-8b)/12b^2-28+6=0

We add all the numbers together, and all the variables

(-3b)/12b^2+(-8b)/12b^2-22=0

We multiply all the terms by the denominator


(-3b)+(-8b)-22*12b^2=0

Wy multiply elements

-264b^2+(-3b)+(-8b)=0

We get rid of parentheses

-264b^2-3b-8b=0

We add all the numbers together, and all the variables

-264b^2-11b=0

a = -264; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-264)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-264}=\frac{0}{-528}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-264}=\frac{22}{-528}
=-1/24
$