3/4m+1/9m-6=15

Solution for 3/4m+1/9m-6=15 equation:

3/4m+1/9m-6=15

We move all terms to the left:

3/4m+1/9m-6-(15)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 9m!=0

m!=0/9

m!=0

m∈R


We add all the numbers together, and all the variables

3/4m+1/9m-21=0

We calculate fractions


27m/36m^2+4m/36m^2-21=0

We multiply all the terms by the denominator


27m+4m-21*36m^2=0

We add all the numbers together, and all the variables

31m-21*36m^2=0

Wy multiply elements

-756m^2+31m=0

a = -756; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-756)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-756}=\frac{-62}{-1512}
=31/756
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-756}=\frac{0}{-1512}
=0
$