2/3x+2x=32

Solution for 2/3x+2x=32 equation:

2/3x+2x=32

We move all terms to the left:

2/3x+2x-(32)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+2/3x-32=0

We multiply all the terms by the denominator


2x*3x-32*3x+2=0

Wy multiply elements

6x^2-96x+2=0

a = 6; b = -96; c = +2;
Δ = b2-4ac
Δ = -962-4·6·2
Δ = 9168
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:

$\sqrt{\Delta}=\sqrt{9168}=\sqrt{16*573}=\sqrt{16}*\sqrt{573}=4\sqrt{573}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{573}}{2*6}=\frac{96-4\sqrt{573}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{573}}{2*6}=\frac{96+4\sqrt{573}}{12}
$