(2x+3)(2x-3)=x+5

Solution for (2x+3)(2x-3)=x+5 equation:

(2x+3)(2x-3)=x+5

We move all terms to the left:

(2x+3)(2x-3)-(x+5)=0

We use the square of the difference formula

4x^2-(x+5)-9=0

We get rid of parentheses

4x^2-x-5-9=0

We add all the numbers together, and all the variables

4x^2-1x-14=0

a = 4; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·4·(-14)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*4}=\frac{-14}{8}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*4}=\frac{16}{8}
=2
$