X-2/3x+2=1

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

X-2/3X+2=1

We move all terms to the left:

X-2/3X+2-(1)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-2/3X+1=0

We multiply all the terms by the denominator


X*3X+1*3X-2=0

Wy multiply elements

3X^2+3X-2=0

a = 3; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·3·(-2)
Δ = 33
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{-(3)-\sqrt{33}}{2*3}=\frac{-3-\sqrt{33}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*3}=\frac{-3+\sqrt{33}}{6}
$