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

Solution for (x-2)2+(x+2)(x-1)-2=3(x+4)(x-3)-x(x-3) equation:

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(3(x+4)(x-3)-x(x-3)), so:

3(x+4)(x-3)-x(x-3)

We multiply parentheses

-x^2+3(x+4)(x-3)+3x

We multiply parentheses ..

-x^2+3(+x^2-3x+4x-12)+3x

We add all the numbers together, and all the variables

-1x^2+3(+x^2-3x+4x-12)+3x

We multiply parentheses

-1x^2+3x^2-9x+12x+3x-36

We add all the numbers together, and all the variables

2x^2+6x-36

Back to the equation:

-(2x^2+6x-36)


We add all the numbers together, and all the variables

(+x^2-1x+2x-2)+2x-(2x^2+6x-36)-6=0

We get rid of parentheses

x^2-2x^2-1x+2x+2x-6x-2+36-6=0

We add all the numbers together, and all the variables

-1x^2-3x+28=0

a = -1; b = -3; c = +28;
Δ = b2-4ac
Δ = -32-4·(-1)·28
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*-1}=\frac{14}{-2}
=-7
$