(3x-11)2=(9x-3)(3x-11)

Solution for (3x-11)2=(9x-3)(3x-11) equation:

(3x-11)2=(9x-3)(3x-11)

We move all terms to the left:

(3x-11)2-((9x-3)(3x-11))=0

We multiply parentheses

6x-((9x-3)(3x-11))-22=0

We multiply parentheses ..

-((+27x^2-99x-9x+33))+6x-22=0


We calculate terms in parentheses: -((+27x^2-99x-9x+33)), so:

(+27x^2-99x-9x+33)

We get rid of parentheses

27x^2-99x-9x+33

We add all the numbers together, and all the variables

27x^2-108x+33

Back to the equation:

-(27x^2-108x+33)


We add all the numbers together, and all the variables

6x-(27x^2-108x+33)-22=0

We get rid of parentheses

-27x^2+6x+108x-33-22=0

We add all the numbers together, and all the variables

-27x^2+114x-55=0

a = -27; b = 114; c = -55;
Δ = b2-4ac
Δ = 1142-4·(-27)·(-55)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-84}{2*-27}=\frac{-198}{-54}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+84}{2*-27}=\frac{-30}{-54}
=5/9
$