4/m+1=7/3m+6

Solution for 4/m+1=7/3m+6 equation:

4/m+1=7/3m+6

We move all terms to the left:

4/m+1-(7/3m+6)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 3m+6)!=0

m∈R


We get rid of parentheses

4/m-7/3m-6+1=0

We calculate fractions


12m/3m^2+(-7m)/3m^2-6+1=0

We add all the numbers together, and all the variables

12m/3m^2+(-7m)/3m^2-5=0

We multiply all the terms by the denominator


12m+(-7m)-5*3m^2=0

Wy multiply elements

-15m^2+12m+(-7m)=0

We get rid of parentheses

-15m^2+12m-7m=0

We add all the numbers together, and all the variables

-15m^2+5m=0

a = -15; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-15)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-15}=\frac{-10}{-30}
=1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-15}=\frac{0}{-30}
=0
$