5/m+1=7/2m+3

Solution for 5/m+1=7/2m+3 equation:

5/m+1=7/2m+3

We move all terms to the left:

5/m+1-(7/2m+3)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 2m+3)!=0

m∈R


We get rid of parentheses

5/m-7/2m-3+1=0

We calculate fractions


10m/2m^2+(-7m)/2m^2-3+1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-4m^2+10m-7m=0

We add all the numbers together, and all the variables

-4m^2+3m=0

a = -4; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-4}=\frac{-6}{-8}
=3/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-4}=\frac{0}{-8}
=0
$