4/m+2+6=3m

Solution for 4/m+2+6=3m equation:

4/m+2+6=3m

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

-3m+4/m+8=0

We multiply all the terms by the denominator


-3m*m+8*m+4=0

We add all the numbers together, and all the variables

8m-3m*m+4=0

Wy multiply elements

-3m^2+8m+4=0

a = -3; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-3)·4
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*-3}=\frac{-8-4\sqrt{7}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*-3}=\frac{-8+4\sqrt{7}}{-6}
$