(x+2)(x+65)=81

Solution for (x+2)(x+65)=81 equation:

(x+2)(x+65)=81

We move all terms to the left:

(x+2)(x+65)-(81)=0

We multiply parentheses ..

(+x^2+65x+2x+130)-81=0

We get rid of parentheses

x^2+65x+2x+130-81=0

We add all the numbers together, and all the variables

x^2+67x+49=0

a = 1; b = 67; c = +49;
Δ = b2-4ac
Δ = 672-4·1·49
Δ = 4293
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:

$\sqrt{\Delta}=\sqrt{4293}=\sqrt{81*53}=\sqrt{81}*\sqrt{53}=9\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-9\sqrt{53}}{2*1}=\frac{-67-9\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+9\sqrt{53}}{2*1}=\frac{-67+9\sqrt{53}}{2}
$