(2x+9)(2x-1)=9

Solution for (2x+9)(2x-1)=9 equation:

(2x+9)(2x-1)=9

We move all terms to the left:

(2x+9)(2x-1)-(9)=0

We multiply parentheses ..

(+4x^2-2x+18x-9)-9=0

We get rid of parentheses

4x^2-2x+18x-9-9=0

We add all the numbers together, and all the variables

4x^2+16x-18=0

a = 4; b = 16; c = -18;
Δ = b2-4ac
Δ = 162-4·4·(-18)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{34}}{2*4}=\frac{-16-4\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{34}}{2*4}=\frac{-16+4\sqrt{34}}{8}
$