x=24/3x+2

Solution for x=24/3x+2 equation:

x=24/3x+2

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

x-24/3x-2=0

We multiply all the terms by the denominator


x*3x-2*3x-24=0

Wy multiply elements

3x^2-6x-24=0

a = 3; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·3·(-24)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*3}=\frac{24}{6}
=4
$