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}
$