4/5m=10m

Solution for 4/5m=10m equation:

4/5m=10m

We move all terms to the left:

4/5m-(10m)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

-10m+4/5m=0

We multiply all the terms by the denominator


-10m*5m+4=0

Wy multiply elements

-50m^2+4=0

a = -50; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-50)·4
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*-50}=\frac{0-20\sqrt{2}}{-100}
=-\frac{20\sqrt{2}}{-100}
=-\frac{\sqrt{2}}{-5}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*-50}=\frac{0+20\sqrt{2}}{-100}
=\frac{20\sqrt{2}}{-100}
=\frac{\sqrt{2}}{-5}
$