(6x-5)(6x+5)=180

Solution for (6x-5)(6x+5)=180 equation:

(6x-5)(6x+5)=180

We move all terms to the left:

(6x-5)(6x+5)-(180)=0

We use the square of the difference formula

36x^2-25-180=0

We add all the numbers together, and all the variables

36x^2-205=0

a = 36; b = 0; c = -205;
Δ = b2-4ac
Δ = 02-4·36·(-205)
Δ = 29520
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:

$\sqrt{\Delta}=\sqrt{29520}=\sqrt{144*205}=\sqrt{144}*\sqrt{205}=12\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{205}}{2*36}=\frac{0-12\sqrt{205}}{72}
=-\frac{12\sqrt{205}}{72}
=-\frac{\sqrt{205}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{205}}{2*36}=\frac{0+12\sqrt{205}}{72}
=\frac{12\sqrt{205}}{72}
=\frac{\sqrt{205}}{6}
$