(2x-3)(2x+3)=81

Solution for (2x-3)(2x+3)=81 equation:

(2x-3)(2x+3)=81

We move all terms to the left:

(2x-3)(2x+3)-(81)=0

We use the square of the difference formula

4x^2-9-81=0

We add all the numbers together, and all the variables

4x^2-90=0

a = 4; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·4·(-90)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*4}=\frac{0-12\sqrt{10}}{8}
=-\frac{12\sqrt{10}}{8}
=-\frac{3\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*4}=\frac{0+12\sqrt{10}}{8}
=\frac{12\sqrt{10}}{8}
=\frac{3\sqrt{10}}{2}
$