2x(x-1)=4+(-x+1)

Solution for 2x(x-1)=4+(-x+1) equation:

2x(x-1)=4+(-x+1)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(4+(-1x+1)), so:

4+(-1x+1)

determiningTheFunctionDomain
(-1x+1)+4

We get rid of parentheses

-1x+1+4

We add all the numbers together, and all the variables

-1x+5

Back to the equation:

-(-1x+5)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-1x-5=0

a = 2; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·2·(-5)
Δ = 41
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{-(-1)-\sqrt{41}}{2*2}=\frac{1-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*2}=\frac{1+\sqrt{41}}{4}
$