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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

2-x(3x+1)

determiningTheFunctionDomain
-x(3x+1)+2

We multiply parentheses

-3x^2-x+2

We add all the numbers together, and all the variables

-3x^2-1x+2

Back to the equation:

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


We add all the numbers together, and all the variables

-(-3x^2-1x+2)+5x-2=0

We get rid of parentheses

3x^2+1x+5x-2-2=0

We add all the numbers together, and all the variables

3x^2+6x-4=0

a = 3; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·3·(-4)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*3}=\frac{-6-2\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*3}=\frac{-6+2\sqrt{21}}{6}
$