d^2-18d+81=14

Solution for d^2-18d+81=14 equation:

d^2-18d+81=14

We move all terms to the left:

d^2-18d+81-(14)=0

We add all the numbers together, and all the variables

d^2-18d+67=0

a = 1; b = -18; c = +67;
Δ = b2-4ac
Δ = -182-4·1·67
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{14}}{2*1}=\frac{18-2\sqrt{14}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{14}}{2*1}=\frac{18+2\sqrt{14}}{2}
$