2x+2(2x+29)=(3x-9)(3x-9)

Solution for 2x+2(2x+29)=(3x-9)(3x-9) equation:

2x+2(2x+29)=(3x-9)(3x-9)

We move all terms to the left:

2x+2(2x+29)-((3x-9)(3x-9))=0

We multiply parentheses

2x+4x-((3x-9)(3x-9))+58=0

We multiply parentheses ..

-((+9x^2-27x-27x+81))+2x+4x+58=0


We calculate terms in parentheses: -((+9x^2-27x-27x+81)), so:

(+9x^2-27x-27x+81)

We get rid of parentheses

9x^2-27x-27x+81

We add all the numbers together, and all the variables

9x^2-54x+81

Back to the equation:

-(9x^2-54x+81)


We add all the numbers together, and all the variables

6x-(9x^2-54x+81)+58=0

We get rid of parentheses

-9x^2+6x+54x-81+58=0

We add all the numbers together, and all the variables

-9x^2+60x-23=0

a = -9; b = 60; c = -23;
Δ = b2-4ac
Δ = 602-4·(-9)·(-23)
Δ = 2772
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:

$\sqrt{\Delta}=\sqrt{2772}=\sqrt{36*77}=\sqrt{36}*\sqrt{77}=6\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-6\sqrt{77}}{2*-9}=\frac{-60-6\sqrt{77}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+6\sqrt{77}}{2*-9}=\frac{-60+6\sqrt{77}}{-18}
$