-4/m-3=-5/5-m

Solution for -4/m-3=-5/5-m equation:

-4/m-3=-5/5-m

We move all terms to the left:

-4/m-3-(-5/5-m)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 5-m)!=0

We move all terms containing m to the left, all other terms to the right

-m)!=-5

m!=-5/1

m!=-5

m∈R


We add all the numbers together, and all the variables

-4/m-(-1m-1)-3=0

We get rid of parentheses

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

We multiply all the terms by the denominator


1m*m+1*m-3*m-4=0

We add all the numbers together, and all the variables

-2m+1m*m-4=0

Wy multiply elements

m^2-2m-4=0

a = 1; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·1·(-4)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*1}=\frac{2-2\sqrt{5}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*1}=\frac{2+2\sqrt{5}}{2}
$