d^2+18d+72=29

Solution for d^2+18d+72=29 equation:

d^2+18d+72=29

We move all terms to the left:

d^2+18d+72-(29)=0

We add all the numbers together, and all the variables

d^2+18d+43=0

a = 1; b = 18; c = +43;
Δ = b2-4ac
Δ = 182-4·1·43
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{38}}{2*1}=\frac{-18-2\sqrt{38}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{38}}{2*1}=\frac{-18+2\sqrt{38}}{2}
$