(x-2)(2x-3)=9x-2

Solution for (x-2)(2x-3)=9x-2 equation:

(x-2)(2x-3)=9x-2

We move all terms to the left:

(x-2)(2x-3)-(9x-2)=0

We get rid of parentheses

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

We multiply parentheses ..

(+2x^2-3x-4x+6)-9x+2=0

We get rid of parentheses

2x^2-3x-4x-9x+6+2=0

We add all the numbers together, and all the variables

2x^2-16x+8=0

a = 2; b = -16; c = +8;
Δ = b2-4ac
Δ = -162-4·2·8
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{3}}{2*2}=\frac{16-8\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{3}}{2*2}=\frac{16+8\sqrt{3}}{4}
$