1/3m.12=84;m=21

Solution for 1/3m.12=84;m=21 equation:

1/3m.12=84m=21

We move all terms to the left:

1/3m.12-(84m)=0


Domain of the equation: 3m.12!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

-84m+1/3m.12=0

We multiply all the terms by the denominator


-84m*3m.12+1=0

Wy multiply elements

-252m^2+1=0

a = -252; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-252)·1
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*-252}=\frac{0-12\sqrt{7}}{-504}
=-\frac{12\sqrt{7}}{-504}
=-\frac{\sqrt{7}}{-42}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*-252}=\frac{0+12\sqrt{7}}{-504}
=\frac{12\sqrt{7}}{-504}
=\frac{\sqrt{7}}{-42}
$