(x-3)(3x-3)=112

Solution for (x-3)(3x-3)=112 equation:

(x-3)(3x-3)=112

We move all terms to the left:

(x-3)(3x-3)-(112)=0

We multiply parentheses ..

(+3x^2-3x-9x+9)-112=0

We get rid of parentheses

3x^2-3x-9x+9-112=0

We add all the numbers together, and all the variables

3x^2-12x-103=0

a = 3; b = -12; c = -103;
Δ = b2-4ac
Δ = -122-4·3·(-103)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{345}}{2*3}=\frac{12-2\sqrt{345}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{345}}{2*3}=\frac{12+2\sqrt{345}}{6}
$