2/3x+3x=22

Solution for 2/3x+3x=22 equation:

2/3x+3x=22

We move all terms to the left:

2/3x+3x-(22)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x-22=0

We multiply all the terms by the denominator


3x*3x-22*3x+2=0

Wy multiply elements

9x^2-66x+2=0

a = 9; b = -66; c = +2;
Δ = b2-4ac
Δ = -662-4·9·2
Δ = 4284
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:

$\sqrt{\Delta}=\sqrt{4284}=\sqrt{36*119}=\sqrt{36}*\sqrt{119}=6\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{119}}{2*9}=\frac{66-6\sqrt{119}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{119}}{2*9}=\frac{66+6\sqrt{119}}{18}
$