4x=24-4/3x

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

4x=24-4/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x+4/3x-24=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-72x+4=0

a = 12; b = -72; c = +4;
Δ = b2-4ac
Δ = -722-4·12·4
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{78}}{2*12}=\frac{72-8\sqrt{78}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{78}}{2*12}=\frac{72+8\sqrt{78}}{24}
$