4=12m+8/m+24

Solution for 4=12m+8/m+24 equation:

4=12m+8/m+24

We move all terms to the left:

4-(12m+8/m+24)=0


Domain of the equation: m+24)!=0

m∈R


We get rid of parentheses

-12m-8/m-24+4=0

We multiply all the terms by the denominator


-12m*m-24*m+4*m-8=0

We add all the numbers together, and all the variables

-20m-12m*m-8=0

Wy multiply elements

-12m^2-20m-8=0

a = -12; b = -20; c = -8;
Δ = b2-4ac
Δ = -202-4·(-12)·(-8)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4}{2*-12}=\frac{16}{-24}
=-2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4}{2*-12}=\frac{24}{-24}
=-1
$