14/4m=16/5m+9

Solution for 14/4m=16/5m+9 equation:

14/4m=16/5m+9

We move all terms to the left:

14/4m-(16/5m+9)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 5m+9)!=0

m∈R


We get rid of parentheses

14/4m-16/5m-9=0

We calculate fractions


70m/20m^2+(-64m)/20m^2-9=0

We multiply all the terms by the denominator


70m+(-64m)-9*20m^2=0

Wy multiply elements

-180m^2+70m+(-64m)=0

We get rid of parentheses

-180m^2+70m-64m=0

We add all the numbers together, and all the variables

-180m^2+6m=0

a = -180; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-180)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-180}=\frac{-12}{-360}
=1/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-180}=\frac{0}{-360}
=0
$