2/(3x+8)=2x+24

Solution for 2/(3x+8)=2x+24 equation:

2/(3x+8)=2x+24

We move all terms to the left:

2/(3x+8)-(2x+24)=0


Domain of the equation: (3x+8)!=0

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

3x!=-8

x!=-8/3

x!=-2+2/3

x∈R


We get rid of parentheses

2/(3x+8)-2x-24=0

We multiply all the terms by the denominator


-2x*(3x+8)-24*(3x+8)+2=0

We multiply parentheses

-6x^2-16x-72x-192+2=0

We add all the numbers together, and all the variables

-6x^2-88x-190=0

a = -6; b = -88; c = -190;
Δ = b2-4ac
Δ = -882-4·(-6)·(-190)
Δ = 3184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{199}}{2*-6}=\frac{88-4\sqrt{199}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{199}}{2*-6}=\frac{88+4\sqrt{199}}{-12}
$