19/3+11/3m=1/4m-2

Solution for 19/3+11/3m=1/4m-2 equation:

19/3+11/3m=1/4m-2

We move all terms to the left:

19/3+11/3m-(1/4m-2)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 4m-2)!=0

m∈R


We get rid of parentheses

11/3m-1/4m+2+19/3=0

We calculate fractions


44m/108m^2+(-27m)/108m^2+76m/108m^2+2=0

We multiply all the terms by the denominator


44m+(-27m)+76m+2*108m^2=0

We add all the numbers together, and all the variables

120m+(-27m)+2*108m^2=0

Wy multiply elements

216m^2+120m+(-27m)=0

We get rid of parentheses

216m^2+120m-27m=0

We add all the numbers together, and all the variables

216m^2+93m=0

a = 216; b = 93; c = 0;
Δ = b2-4ac
Δ = 932-4·216·0
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-93}{2*216}=\frac{-186}{432}
=-31/72
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+93}{2*216}=\frac{0}{432}
=0
$