(5x-2)(5x+2)=180

Solution for (5x-2)(5x+2)=180 equation:

(5x-2)(5x+2)=180

We move all terms to the left:

(5x-2)(5x+2)-(180)=0

We use the square of the difference formula

25x^2-4-180=0

We add all the numbers together, and all the variables

25x^2-184=0

a = 25; b = 0; c = -184;
Δ = b2-4ac
Δ = 02-4·25·(-184)
Δ = 18400
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:

$\sqrt{\Delta}=\sqrt{18400}=\sqrt{400*46}=\sqrt{400}*\sqrt{46}=20\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{46}}{2*25}=\frac{0-20\sqrt{46}}{50}
=-\frac{20\sqrt{46}}{50}
=-\frac{2\sqrt{46}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{46}}{2*25}=\frac{0+20\sqrt{46}}{50}
=\frac{20\sqrt{46}}{50}
=\frac{2\sqrt{46}}{5}
$