2/3m=20m=

Solution for 2/3m=20m= equation:

2/3m=20m=

We move all terms to the left:

2/3m-(20m)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

-20m+2/3m=0

We multiply all the terms by the denominator


-20m*3m+2=0

Wy multiply elements

-60m^2+2=0

a = -60; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-60)·2
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-60}=\frac{0-4\sqrt{30}}{-120}
=-\frac{4\sqrt{30}}{-120}
=-\frac{\sqrt{30}}{-30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-60}=\frac{0+4\sqrt{30}}{-120}
=\frac{4\sqrt{30}}{-120}
=\frac{\sqrt{30}}{-30}
$