(x-3)(2x-3)=12

Solution for (x-3)(2x-3)=12 equation:

(x-3)(2x-3)=12

We move all terms to the left:

(x-3)(2x-3)-(12)=0

We multiply parentheses ..

(+2x^2-3x-6x+9)-12=0

We get rid of parentheses

2x^2-3x-6x+9-12=0

We add all the numbers together, and all the variables

2x^2-9x-3=0

a = 2; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·2·(-3)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{105}}{2*2}=\frac{9-\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*2}=\frac{9+\sqrt{105}}{4}
$