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

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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 $

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