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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+9x^2-27x-27x+81)-(2x+2(2x+29))=0


We calculate terms in parentheses: -(2x+2(2x+29)), so:

2x+2(2x+29)

We multiply parentheses

2x+4x+58

We add all the numbers together, and all the variables

6x+58

Back to the equation:

-(6x+58)


We get rid of parentheses

9x^2-27x-27x-6x+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}
$