1/3m+2/3m=16-m

Solution for 1/3m+2/3m=16-m equation:

1/3m+2/3m=16-m

We move all terms to the left:

1/3m+2/3m-(16-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

1/3m+2/3m-(-1m+16)=0

We get rid of parentheses

1/3m+2/3m+1m-16=0

We multiply all the terms by the denominator


1m*3m-16*3m+1+2=0

We add all the numbers together, and all the variables

1m*3m-16*3m+3=0

Wy multiply elements

3m^2-48m+3=0

a = 3; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·3·3
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-18\sqrt{7}}{2*3}=\frac{48-18\sqrt{7}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+18\sqrt{7}}{2*3}=\frac{48+18\sqrt{7}}{6}
$