4/m-4=2/5m

Solution for 4/m-4=2/5m equation:

4/m-4=2/5m

We move all terms to the left:

4/m-4-(2/5m)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 5m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

4/m-(+2/5m)-4=0

We get rid of parentheses

4/m-2/5m-4=0

We calculate fractions


20m/5m^2+(-2m)/5m^2-4=0

We multiply all the terms by the denominator


20m+(-2m)-4*5m^2=0

Wy multiply elements

-20m^2+20m+(-2m)=0

We get rid of parentheses

-20m^2+20m-2m=0

We add all the numbers together, and all the variables

-20m^2+18m=0

a = -20; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-20)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-20}=\frac{-36}{-40}
=9/10
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-20}=\frac{0}{-40}
=0
$