x+3x-6+2/3x+2=150

Solution for x+3x-6+2/3x+2=150 equation:

x+3x-6+2/3x+2=150

We move all terms to the left:

x+3x-6+2/3x+2-(150)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x+2/3x-154=0

We multiply all the terms by the denominator


4x*3x-154*3x+2=0

Wy multiply elements

12x^2-462x+2=0

a = 12; b = -462; c = +2;
Δ = b2-4ac
Δ = -4622-4·12·2
Δ = 213348
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:

$\sqrt{\Delta}=\sqrt{213348}=\sqrt{4*53337}=\sqrt{4}*\sqrt{53337}=2\sqrt{53337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-462)-2\sqrt{53337}}{2*12}=\frac{462-2\sqrt{53337}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-462)+2\sqrt{53337}}{2*12}=\frac{462+2\sqrt{53337}}{24}
$