6/3m+1=9/5m+3

Solution for 6/3m+1=9/5m+3 equation:

6/3m+1=9/5m+3

We move all terms to the left:

6/3m+1-(9/5m+3)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 5m+3)!=0

m∈R


We get rid of parentheses

6/3m-9/5m-3+1=0

We calculate fractions


30m/15m^2+(-27m)/15m^2-3+1=0

We add all the numbers together, and all the variables

30m/15m^2+(-27m)/15m^2-2=0

We multiply all the terms by the denominator


30m+(-27m)-2*15m^2=0

Wy multiply elements

-30m^2+30m+(-27m)=0

We get rid of parentheses

-30m^2+30m-27m=0

We add all the numbers together, and all the variables

-30m^2+3m=0

a = -30; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-30)·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*-30}=\frac{-6}{-60}
=1/10
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-30}=\frac{0}{-60}
=0
$