d^2-18d=29

Solution for d^2-18d=29 equation:

d^2-18d=29

We move all terms to the left:

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

a = 1; b = -18; c = -29;
Δ = b2-4ac
Δ = -182-4·1·(-29)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{110}}{2*1}=\frac{18-2\sqrt{110}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{110}}{2*1}=\frac{18+2\sqrt{110}}{2}
$