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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2-1x-4x+4)), so:

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

We get rid of parentheses

x^2-1x-4x+4

We add all the numbers together, and all the variables

x^2-5x+4

Back to the equation:

-(x^2-5x+4)


We add all the numbers together, and all the variables

4x-(x^2-5x+4)+2=0

We get rid of parentheses

-x^2+4x+5x-4+2=0

We add all the numbers together, and all the variables

-1x^2+9x-2=0

a = -1; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-1)·(-2)
Δ = 73
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{-(9)-\sqrt{73}}{2*-1}=\frac{-9-\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{73}}{2*-1}=\frac{-9+\sqrt{73}}{-2}
$