9(9+20)=(x-2)(x+6)

Solution for 9(9+20)=(x-2)(x+6) equation:

9(9+20)=(x-2)(x+6)

We move all terms to the left:

9(9+20)-((x-2)(x+6))=0

We add all the numbers together, and all the variables

-((x-2)(x+6))+929=0

We multiply parentheses ..

-((+x^2+6x-2x-12))+929=0


We calculate terms in parentheses: -((+x^2+6x-2x-12)), so:

(+x^2+6x-2x-12)

We get rid of parentheses

x^2+6x-2x-12

We add all the numbers together, and all the variables

x^2+4x-12

Back to the equation:

-(x^2+4x-12)


We get rid of parentheses

-x^2-4x+12+929=0

We add all the numbers together, and all the variables

-1x^2-4x+941=0

a = -1; b = -4; c = +941;
Δ = b2-4ac
Δ = -42-4·(-1)·941
Δ = 3780
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{105}}{2*-1}=\frac{4-6\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{105}}{2*-1}=\frac{4+6\sqrt{105}}{-2}
$