102/3m=m

Solution for 102/3m=m equation:

102/3m=m

We move all terms to the left:

102/3m-(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

-1m+102/3m=0

We multiply all the terms by the denominator


-1m*3m+102=0

Wy multiply elements

-3m^2+102=0

a = -3; b = 0; c = +102;
Δ = b2-4ac
Δ = 02-4·(-3)·102
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{34}}{2*-3}=\frac{0-6\sqrt{34}}{-6}
=-\frac{6\sqrt{34}}{-6}
=-\frac{\sqrt{34}}{-1}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{34}}{2*-3}=\frac{0+6\sqrt{34}}{-6}
=\frac{6\sqrt{34}}{-6}
=\frac{\sqrt{34}}{-1}
$