(5-9m)/m^2-36=0

Solution for (5-9m)/m^2-36=0 equation:

(5-9m)/m^2-36=0


Domain of the equation: m^2!=0

m^2!=0/

m^2!=√0

m!=0

m∈R


We add all the numbers together, and all the variables

(-9m+5)/m^2-36=0

We multiply all the terms by the denominator


(-9m+5)-36*m^2=0

We add all the numbers together, and all the variables

-36m^2+(-9m+5)=0

We get rid of parentheses

-36m^2-9m+5=0

a = -36; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·(-36)·5
Δ = 801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{89}}{2*-36}=\frac{9-3\sqrt{89}}{-72}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{89}}{2*-36}=\frac{9+3\sqrt{89}}{-72}
$