d*d-10*d+19=0

Solution for d*d-10*d+19=0 equation:

d*d-10d+19=0

We add all the numbers together, and all the variables

-10d+d*d+19=0

Wy multiply elements

d^2-10d+19=0

a = 1; b = -10; c = +19;
Δ = b2-4ac
Δ = -102-4·1·19
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{6}}{2*1}=\frac{10-2\sqrt{6}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{6}}{2*1}=\frac{10+2\sqrt{6}}{2}
$