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

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}
$