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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We multiply parentheses ..

-((+4x^2-8x+9x-18))-4x+2x+4=0


We calculate terms in parentheses: -((+4x^2-8x+9x-18)), so:

(+4x^2-8x+9x-18)

We get rid of parentheses

4x^2-8x+9x-18

We add all the numbers together, and all the variables

4x^2+x-18

Back to the equation:

-(4x^2+x-18)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-4x^2-2x-x+18+4=0

We add all the numbers together, and all the variables

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

a = -4; b = -3; c = +22;
Δ = b2-4ac
Δ = -32-4·(-4)·22
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-19}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+19}{2*-4}=\frac{22}{-8}
=-2+3/4
$