4/3x+x=12

Solution for 4/3x+x=12 equation:

4/3x+x=12

We move all terms to the left:

4/3x+x-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/3x-12=0

We multiply all the terms by the denominator


x*3x-12*3x+4=0

Wy multiply elements

3x^2-36x+4=0

a = 3; b = -36; c = +4;
Δ = b2-4ac
Δ = -362-4·3·4
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{78}}{2*3}=\frac{36-4\sqrt{78}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{78}}{2*3}=\frac{36+4\sqrt{78}}{6}
$