2/5m-3=1/2m+4

Solution for 2/5m-3=1/2m+4 equation:

2/5m-3=1/2m+4

We move all terms to the left:

2/5m-3-(1/2m+4)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 2m+4)!=0

m∈R


We get rid of parentheses

2/5m-1/2m-4-3=0

We calculate fractions


4m/10m^2+(-5m)/10m^2-4-3=0

We add all the numbers together, and all the variables

4m/10m^2+(-5m)/10m^2-7=0

We multiply all the terms by the denominator


4m+(-5m)-7*10m^2=0

Wy multiply elements

-70m^2+4m+(-5m)=0

We get rid of parentheses

-70m^2+4m-5m=0

We add all the numbers together, and all the variables

-70m^2-1m=0

a = -70; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-70)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-70}=\frac{0}{-140}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-70}=\frac{2}{-140}
=-1/70
$