x-4=8/3x-24

Solution for x-4=8/3x-24 equation:

x-4=8/3x-24

We move all terms to the left:

x-4-(8/3x-24)=0


Domain of the equation: 3x-24)!=0

x∈R


We get rid of parentheses

x-8/3x+24-4=0

We multiply all the terms by the denominator


x*3x+24*3x-4*3x-8=0

Wy multiply elements

3x^2+72x-12x-8=0

We add all the numbers together, and all the variables

3x^2+60x-8=0

a = 3; b = 60; c = -8;
Δ = b2-4ac
Δ = 602-4·3·(-8)
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{231}}{2*3}=\frac{-60-4\sqrt{231}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{231}}{2*3}=\frac{-60+4\sqrt{231}}{6}
$