4=12x+8/x+24

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

4=12x+8/x+24

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-20x-12x*x-8=0

Wy multiply elements

-12x^2-20x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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