1/3m+m=120

Solution for 1/3m+m=120 equation:

1/3m+m=120

We move all terms to the left:

1/3m+m-(120)=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+1/3m-120=0

We multiply all the terms by the denominator


m*3m-120*3m+1=0

Wy multiply elements

3m^2-360m+1=0

a = 3; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·3·1
Δ = 129588
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:

$\sqrt{\Delta}=\sqrt{129588}=\sqrt{4*32397}=\sqrt{4}*\sqrt{32397}=2\sqrt{32397}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32397}}{2*3}=\frac{360-2\sqrt{32397}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32397}}{2*3}=\frac{360+2\sqrt{32397}}{6}
$