(5p+8)(5p-8)=9

Solution for (5p+8)(5p-8)=9 equation:

(5p+8)(5p-8)=9

We move all terms to the left:

(5p+8)(5p-8)-(9)=0

We use the square of the difference formula

25p^2-64-9=0

We add all the numbers together, and all the variables

25p^2-73=0

a = 25; b = 0; c = -73;
Δ = b2-4ac
Δ = 02-4·25·(-73)
Δ = 7300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{73}}{2*25}=\frac{0-10\sqrt{73}}{50}
=-\frac{10\sqrt{73}}{50}
=-\frac{\sqrt{73}}{5}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{73}}{2*25}=\frac{0+10\sqrt{73}}{50}
=\frac{10\sqrt{73}}{50}
=\frac{\sqrt{73}}{5}
$