(3x-1)(3x-1)-64=0

Solution for (3x-1)(3x-1)-64=0 equation:

(3x-1)(3x-1)-64=0

We multiply parentheses ..

(+9x^2-3x-3x+1)-64=0

We get rid of parentheses

9x^2-3x-3x+1-64=0

We add all the numbers together, and all the variables

9x^2-6x-63=0

a = 9; b = -6; c = -63;
Δ = b2-4ac
Δ = -62-4·9·(-63)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-48}{2*9}=\frac{-42}{18}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+48}{2*9}=\frac{54}{18}
=3
$