4/3m=-m+5/3m+3

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Solution for 4/3m=-m+5/3m+3 equation:



4/3m=-m+5/3m+3
We move all terms to the left:
4/3m-(-m+5/3m+3)=0
Domain of the equation: 3m!=0
m!=0/3
m!=0
m∈R
Domain of the equation: 3m+3)!=0
m∈R
We add all the numbers together, and all the variables
4/3m-(-1m+5/3m+3)=0
We get rid of parentheses
4/3m+1m-5/3m-3=0
We multiply all the terms by the denominator
1m*3m-3*3m+4-5=0
We add all the numbers together, and all the variables
1m*3m-3*3m-1=0
Wy multiply elements
3m^2-9m-1=0
a = 3; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·3·(-1)
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{93}}{2*3}=\frac{9-\sqrt{93}}{6} $
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{93}}{2*3}=\frac{9+\sqrt{93}}{6} $

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