d^2-20d=50

Solution for d^2-20d=50 equation:

d^2-20d=50

We move all terms to the left:

d^2-20d-(50)=0

a = 1; b = -20; c = -50;
Δ = b2-4ac
Δ = -202-4·1·(-50)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{6}}{2*1}=\frac{20-10\sqrt{6}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{6}}{2*1}=\frac{20+10\sqrt{6}}{2}
$