(x-9)(x-9)+2x(x-9)=(4+x)(4-x)

Solution for (x-9)(x-9)+2x(x-9)=(4+x)(4-x) equation:

(x-9)(x-9)+2x(x-9)=(4+x)(4-x)

We move all terms to the left:

(x-9)(x-9)+2x(x-9)-((4+x)(4-x))=0

We add all the numbers together, and all the variables

(x-9)(x-9)+2x(x-9)-((x+4)(-1x+4))=0

We multiply parentheses

2x^2+(x-9)(x-9)-18x-((x+4)(-1x+4))=0

We multiply parentheses ..

2x^2+(+x^2-9x-9x+81)-18x-((x+4)(-1x+4))=0


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

(x+4)(-1x+4)

We multiply parentheses ..

(-1x^2+4x-4x+16)

We get rid of parentheses

-1x^2+4x-4x+16

We add all the numbers together, and all the variables

-1x^2+16

Back to the equation:

-(-1x^2+16)


We get rid of parentheses

2x^2+x^2+1x^2-9x-9x-18x+81-16=0

We add all the numbers together, and all the variables

4x^2-36x+65=0

a = 4; b = -36; c = +65;
Δ = b2-4ac
Δ = -362-4·4·65
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16}{2*4}=\frac{20}{8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16}{2*4}=\frac{52}{8}
=6+1/2
$