x2-6x+9=(5X+1)(X-3)

Solution for x2-6x+9=(5X+1)(X-3) equation:

x2-6x+9=(5x+1)(x-3)

We move all terms to the left:

x2-6x+9-((5x+1)(x-3))=0

We add all the numbers together, and all the variables

x^2-6x-((5x+1)(x-3))+9=0

We multiply parentheses ..

x^2-((+5x^2-15x+x-3))-6x+9=0


We calculate terms in parentheses: -((+5x^2-15x+x-3)), so:

(+5x^2-15x+x-3)

We get rid of parentheses

5x^2-15x+x-3

We add all the numbers together, and all the variables

5x^2-14x-3

Back to the equation:

-(5x^2-14x-3)


We add all the numbers together, and all the variables

x^2-6x-(5x^2-14x-3)+9=0

We get rid of parentheses

x^2-5x^2-6x+14x+3+9=0

We add all the numbers together, and all the variables

-4x^2+8x+12=0

a = -4; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·(-4)·12
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{-(8)-16}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*-4}=\frac{8}{-8}
=-1
$