(x-3)(3x-3)=17

Solution for (x-3)(3x-3)=17 equation:

(x-3)(3x-3)=17

We move all terms to the left:

(x-3)(3x-3)-(17)=0

We multiply parentheses ..

(+3x^2-3x-9x+9)-17=0

We get rid of parentheses

3x^2-3x-9x+9-17=0

We add all the numbers together, and all the variables

3x^2-12x-8=0

a = 3; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·3·(-8)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*3}=\frac{12-4\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*3}=\frac{12+4\sqrt{15}}{6}
$