2x(2x-3)=9

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

2x(2x-3)=9

We move all terms to the left:

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

We multiply parentheses

4x^2-6x-9=0

a = 4; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·4·(-9)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*4}=\frac{6-6\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*4}=\frac{6+6\sqrt{5}}{8}
$