4/m-5=m-6

Solution for 4/m-5=m-6 equation:

4/m-5=m-6

We move all terms to the left:

4/m-5-(m-6)=0


Domain of the equation: m!=0

m∈R


We get rid of parentheses

4/m-m+6-5=0

We multiply all the terms by the denominator


-m*m+6*m-5*m+4=0

We add all the numbers together, and all the variables

m-m*m+4=0

Wy multiply elements

-1m^2+m+4=0

a = -1; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-1)·4
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{17}}{2*-1}=\frac{-1-\sqrt{17}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*-1}=\frac{-1+\sqrt{17}}{-2}
$