200*6m=500/6m

Solution for 200*6m=500/6m equation:

200*6m=500/6m

We move all terms to the left:

200*6m-(500/6m)=0


Domain of the equation: 6m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

200*6m-(+500/6m)=0

Wy multiply elements

1200m-(+500/6m)=0

We get rid of parentheses

1200m-500/6m=0

We multiply all the terms by the denominator


1200m*6m-500=0

Wy multiply elements

7200m^2-500=0

a = 7200; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·7200·(-500)
Δ = 14400000
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:

$\sqrt{\Delta}=\sqrt{14400000}=\sqrt{1440000*10}=\sqrt{1440000}*\sqrt{10}=1200\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1200\sqrt{10}}{2*7200}=\frac{0-1200\sqrt{10}}{14400}
=-\frac{1200\sqrt{10}}{14400}
=-\frac{\sqrt{10}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1200\sqrt{10}}{2*7200}=\frac{0+1200\sqrt{10}}{14400}
=\frac{1200\sqrt{10}}{14400}
=\frac{\sqrt{10}}{12}
$