6(m-2)-4(m+1)/3m+1;m=3

Solution for 6(m-2)-4(m+1)/3m+1;m=3 equation:

6(m-2)-4(m+1)/3m+1m=3

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

m+6(m-2)-4(m+1)/3m-3=0

We multiply parentheses

m+6m-4(m+1)/3m-12-3=0

We multiply all the terms by the denominator


m*3m+6m*3m-4(m+1)-12*3m-3*3m=0

We multiply parentheses

m*3m+6m*3m-4m-12*3m-3*3m-4=0

Wy multiply elements

3m^2+18m^2-4m-36m-9m-4=0

We add all the numbers together, and all the variables

21m^2-49m-4=0

a = 21; b = -49; c = -4;
Δ = b2-4ac
Δ = -492-4·21·(-4)
Δ = 2737
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{-(-49)-\sqrt{2737}}{2*21}=\frac{49-\sqrt{2737}}{42}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2737}}{2*21}=\frac{49+\sqrt{2737}}{42}
$