3x-9(3x-9)=(2x+2)(2x+2+25)

Solution for 3x-9(3x-9)=(2x+2)(2x+2+25) equation:

3x-9(3x-9)=(2x+2)(2x+2+25)

We move all terms to the left:

3x-9(3x-9)-((2x+2)(2x+2+25))=0

We add all the numbers together, and all the variables

3x-9(3x-9)-((2x+2)(2x+27))=0

We multiply parentheses

3x-27x-((2x+2)(2x+27))+81=0

We multiply parentheses ..

-((+4x^2+54x+4x+54))+3x-27x+81=0


We calculate terms in parentheses: -((+4x^2+54x+4x+54)), so:

(+4x^2+54x+4x+54)

We get rid of parentheses

4x^2+54x+4x+54

We add all the numbers together, and all the variables

4x^2+58x+54

Back to the equation:

-(4x^2+58x+54)


We add all the numbers together, and all the variables

-24x-(4x^2+58x+54)+81=0

We get rid of parentheses

-4x^2-24x-58x-54+81=0

We add all the numbers together, and all the variables

-4x^2-82x+27=0

a = -4; b = -82; c = +27;
Δ = b2-4ac
Δ = -822-4·(-4)·27
Δ = 7156
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:

$\sqrt{\Delta}=\sqrt{7156}=\sqrt{4*1789}=\sqrt{4}*\sqrt{1789}=2\sqrt{1789}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1789}}{2*-4}=\frac{82-2\sqrt{1789}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1789}}{2*-4}=\frac{82+2\sqrt{1789}}{-8}
$