2/3m+3=m-4

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

2/3m+3=m-4

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3m^2+12m+9m+2=0

We add all the numbers together, and all the variables

-3m^2+21m+2=0

a = -3; b = 21; c = +2;
Δ = b2-4ac
Δ = 212-4·(-3)·2
Δ = 465
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{-(21)-\sqrt{465}}{2*-3}=\frac{-21-\sqrt{465}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{465}}{2*-3}=\frac{-21+\sqrt{465}}{-6}
$