(2x-3)(4x-3)=9

Solution for (2x-3)(4x-3)=9 equation:

(2x-3)(4x-3)=9

We move all terms to the left:

(2x-3)(4x-3)-(9)=0

We multiply parentheses ..

(+8x^2-6x-12x+9)-9=0

We get rid of parentheses

8x^2-6x-12x+9-9=0

We add all the numbers together, and all the variables

8x^2-18x=0

a = 8; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·8·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*8}=\frac{36}{16}
=2+1/4
$