(x-2)(x-2)-3(x+2)=2(x-11)

Solution for (x-2)(x-2)-3(x+2)=2(x-11) equation:

(x-2)(x-2)-3(x+2)=2(x-11)

We move all terms to the left:

(x-2)(x-2)-3(x+2)-(2(x-11))=0

We multiply parentheses

(x-2)(x-2)-3x-(2(x-11))-6=0

We multiply parentheses ..

(+x^2-2x-2x+4)-3x-(2(x-11))-6=0


We calculate terms in parentheses: -(2(x-11)), so:

2(x-11)

We multiply parentheses

2x-22

Back to the equation:

-(2x-22)


We get rid of parentheses

x^2-2x-2x-3x-2x+4+22-6=0

We add all the numbers together, and all the variables

x^2-9x+20=0

a = 1; b = -9; c = +20;
Δ = b2-4ac
Δ = -92-4·1·20
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*1}=\frac{10}{2}
=5
$