-x=22-1/3x

Solution for -x=22-1/3x equation:

-x=22-1/3x

We move all terms to the left:

-x-(22-1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(-1/3x+22)=0

We add all the numbers together, and all the variables

-1x-(-1/3x+22)=0

We get rid of parentheses

-1x+1/3x-22=0

We multiply all the terms by the denominator


-1x*3x-22*3x+1=0

Wy multiply elements

-3x^2-66x+1=0

a = -3; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·(-3)·1
Δ = 4368
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:

$\sqrt{\Delta}=\sqrt{4368}=\sqrt{16*273}=\sqrt{16}*\sqrt{273}=4\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-4\sqrt{273}}{2*-3}=\frac{66-4\sqrt{273}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+4\sqrt{273}}{2*-3}=\frac{66+4\sqrt{273}}{-6}
$