M(1/3)m=1200

Solution for M(1/3)m=1200 equation:

(1/3)M=1200

We move all terms to the left:

(1/3)M-(1200)=0


Domain of the equation: 3)M!=0

M!=0/1

M!=0

M∈R


We add all the numbers together, and all the variables

(+1/3)M-1200=0

We multiply parentheses

M^2-1200=0

a = 1; b = 0; c = -1200;
Δ = b2-4ac
Δ = 02-4·1·(-1200)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*1}=\frac{0-40\sqrt{3}}{2}
=-\frac{40\sqrt{3}}{2}
=-20\sqrt{3}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*1}=\frac{0+40\sqrt{3}}{2}
=\frac{40\sqrt{3}}{2}
=20\sqrt{3}
$