1-x^2/3-3x+2/3=1

Solution for 1-x^2/3-3x+2/3=1 equation:

1-x^2/3-3x+2/3=1

We move all terms to the left:

1-x^2/3-3x+2/3-(1)=0

determiningTheFunctionDomain
-x^2/3-3x+1-1+2/3=0

We add all the numbers together, and all the variables

-x^2/3-3x+2/3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-1x^2-9x+2=0

a = -1; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-1)·2
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{89}}{2*-1}=\frac{9-\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{89}}{2*-1}=\frac{9+\sqrt{89}}{-2}
$