-x+3=2/3x-2

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

-x+3=2/3x-2

We move all terms to the left:

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


Domain of the equation: 3x-2)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+6x+9x-2=0

We add all the numbers together, and all the variables

-3x^2+15x-2=0

a = -3; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·(-3)·(-2)
Δ = 201
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{-(15)-\sqrt{201}}{2*-3}=\frac{-15-\sqrt{201}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*-3}=\frac{-15+\sqrt{201}}{-6}
$