2/3m-4=6+m

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

2/3m-4=6+m

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/3m-m-6-4=0

We multiply all the terms by the denominator


-m*3m-6*3m-4*3m+2=0

Wy multiply elements

-3m^2-18m-12m+2=0

We add all the numbers together, and all the variables

-3m^2-30m+2=0

a = -3; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·(-3)·2
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{231}}{2*-3}=\frac{30-2\sqrt{231}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{231}}{2*-3}=\frac{30+2\sqrt{231}}{-6}
$