(4-m)/m+11=2/3m

Solution for (4-m)/m+11=2/3m equation:

(4-m)/m+11=2/3m

We move all terms to the left:

(4-m)/m+11-(2/3m)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 3m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

(-1m+4)/m-(+2/3m)+11=0

We get rid of parentheses

(-1m+4)/m-2/3m+11=0

We calculate fractions


(-3m^2+12m)/3m^2+(-2m)/3m^2+11=0

We multiply all the terms by the denominator


(-3m^2+12m)+(-2m)+11*3m^2=0

Wy multiply elements

(-3m^2+12m)+33m^2+(-2m)=0

We get rid of parentheses

-3m^2+33m^2+12m-2m=0

We add all the numbers together, and all the variables

30m^2+10m=0

a = 30; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·30·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*30}=\frac{-20}{60}
=-1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*30}=\frac{0}{60}
=0
$