4=4x+1/3x-4

Solution for 4=4x+1/3x-4 equation:

4=4x+1/3x-4

We move all terms to the left:

4-(4x+1/3x-4)=0


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

-4x-1/3x+4+4=0

We multiply all the terms by the denominator


-4x*3x+4*3x+4*3x-1=0

Wy multiply elements

-12x^2+12x+12x-1=0

We add all the numbers together, and all the variables

-12x^2+24x-1=0

a = -12; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-12)·(-1)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{33}}{2*-12}=\frac{-24-4\sqrt{33}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{33}}{2*-12}=\frac{-24+4\sqrt{33}}{-24}
$