(6x+1)(6x-3)=82

Solution for (6x+1)(6x-3)=82 equation:

(6x+1)(6x-3)=82

We move all terms to the left:

(6x+1)(6x-3)-(82)=0

We multiply parentheses ..

(+36x^2-18x+6x-3)-82=0

We get rid of parentheses

36x^2-18x+6x-3-82=0

We add all the numbers together, and all the variables

36x^2-12x-85=0

a = 36; b = -12; c = -85;
Δ = b2-4ac
Δ = -122-4·36·(-85)
Δ = 12384
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:

$\sqrt{\Delta}=\sqrt{12384}=\sqrt{144*86}=\sqrt{144}*\sqrt{86}=12\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{86}}{2*36}=\frac{12-12\sqrt{86}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{86}}{2*36}=\frac{12+12\sqrt{86}}{72}
$