(d-2)(d-6)=83

Solution for (d-2)(d-6)=83 equation:

(d-2)(d-6)=83

We move all terms to the left:

(d-2)(d-6)-(83)=0

We multiply parentheses ..

(+d^2-6d-2d+12)-83=0

We get rid of parentheses

d^2-6d-2d+12-83=0

We add all the numbers together, and all the variables

d^2-8d-71=0

a = 1; b = -8; c = -71;
Δ = b2-4ac
Δ = -82-4·1·(-71)
Δ = 348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{87}}{2*1}=\frac{8-2\sqrt{87}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{87}}{2*1}=\frac{8+2\sqrt{87}}{2}
$