2x+24=4/9x

Solution for 2x+24=4/9x equation:

2x+24=4/9x

We move all terms to the left:

2x+24-(4/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+4/9x)+24=0

We get rid of parentheses

2x-4/9x+24=0

We multiply all the terms by the denominator


2x*9x+24*9x-4=0

Wy multiply elements

18x^2+216x-4=0

a = 18; b = 216; c = -4;
Δ = b2-4ac
Δ = 2162-4·18·(-4)
Δ = 46944
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:

$\sqrt{\Delta}=\sqrt{46944}=\sqrt{144*326}=\sqrt{144}*\sqrt{326}=12\sqrt{326}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-12\sqrt{326}}{2*18}=\frac{-216-12\sqrt{326}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+12\sqrt{326}}{2*18}=\frac{-216+12\sqrt{326}}{36}
$