3-x(1-3x)=5-(1-2x)

Solution for 3-x(1-3x)=5-(1-2x) equation:

3-x(1-3x)=5-(1-2x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(5-(-2x+1)), so:

5-(-2x+1)

determiningTheFunctionDomain
-(-2x+1)+5

We get rid of parentheses

2x-1+5

We add all the numbers together, and all the variables

2x+4

Back to the equation:

-(2x+4)


We add all the numbers together, and all the variables

3x^2-1x-(2x+4)+3=0

We get rid of parentheses

3x^2-1x-2x-4+3=0

We add all the numbers together, and all the variables

3x^2-3x-1=0

a = 3; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·3·(-1)
Δ = 21
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{21}}{2*3}=\frac{3-\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*3}=\frac{3+\sqrt{21}}{6}
$