4/3b=1/4b+3

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



4/3b=1/4b+3
We move all terms to the left:
4/3b-(1/4b+3)=0
Domain of the equation: 3b!=0
b!=0/3
b!=0
b∈R
Domain of the equation: 4b+3)!=0
b∈R
We get rid of parentheses
4/3b-1/4b-3=0
We calculate fractions
16b/12b^2+(-3b)/12b^2-3=0
We multiply all the terms by the denominator
16b+(-3b)-3*12b^2=0
Wy multiply elements
-36b^2+16b+(-3b)=0
We get rid of parentheses
-36b^2+16b-3b=0
We add all the numbers together, and all the variables
-36b^2+13b=0
a = -36; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-36)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-36}=\frac{-26}{-72} =13/36 $
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-36}=\frac{0}{-72} =0 $

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