(3x-4)(3x-4)=81

Solution for (3x-4)(3x-4)=81 equation:

(3x-4)(3x-4)=81

We move all terms to the left:

(3x-4)(3x-4)-(81)=0

We multiply parentheses ..

(+9x^2-12x-12x+16)-81=0

We get rid of parentheses

9x^2-12x-12x+16-81=0

We add all the numbers together, and all the variables

9x^2-24x-65=0

a = 9; b = -24; c = -65;
Δ = b2-4ac
Δ = -242-4·9·(-65)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-54}{2*9}=\frac{-30}{18}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+54}{2*9}=\frac{78}{18}
=4+1/3
$