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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -((+x^2+1-2x*3*2)), so:

(+x^2+1-2x*3*2)

We get rid of parentheses

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

Wy multiply elements

x^2-12x*2+1

Wy multiply elements

x^2-24x+1

Back to the equation:

-(x^2-24x+1)


We add all the numbers together, and all the variables

-(x^2-24x+1)=0

We get rid of parentheses

-x^2+24x-1=0

We add all the numbers together, and all the variables

-1x^2+24x-1=0

a = -1; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-1)·(-1)
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{143}}{2*-1}=\frac{-24-2\sqrt{143}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{143}}{2*-1}=\frac{-24+2\sqrt{143}}{-2}
$