x=2/3x-24

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

x=2/3x-24

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-2/3x+24=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+72x-2=0

a = 3; b = 72; c = -2;
Δ = b2-4ac
Δ = 722-4·3·(-2)
Δ = 5208
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:

$\sqrt{\Delta}=\sqrt{5208}=\sqrt{4*1302}=\sqrt{4}*\sqrt{1302}=2\sqrt{1302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1302}}{2*3}=\frac{-72-2\sqrt{1302}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1302}}{2*3}=\frac{-72+2\sqrt{1302}}{6}
$