d2=172

Solution for d2=172 equation:

d2=172

We move all terms to the left:

d2-(172)=0

We add all the numbers together, and all the variables

d^2-172=0

a = 1; b = 0; c = -172;
Δ = b2-4ac
Δ = 02-4·1·(-172)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{43}}{2*1}=\frac{0-4\sqrt{43}}{2}
=-\frac{4\sqrt{43}}{2}
=-2\sqrt{43}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{43}}{2*1}=\frac{0+4\sqrt{43}}{2}
=\frac{4\sqrt{43}}{2}
=2\sqrt{43}
$