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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

6x^2-1x+2x-(3-2(2x+2))=0


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

3-2(2x+2)

determiningTheFunctionDomain
-2(2x+2)+3

We multiply parentheses

-4x-4+3

We add all the numbers together, and all the variables

-4x-1

Back to the equation:

-(-4x-1)


We add all the numbers together, and all the variables

6x^2+x-(-4x-1)=0

We get rid of parentheses

6x^2+x+4x+1=0

We add all the numbers together, and all the variables

6x^2+5x+1=0

a = 6; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·6·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*6}=\frac{-4}{12}
=-1/3
$