42=d^2-22d=

Solution for 42=d^2-22d= equation:

42=d^2-22d=

We move all terms to the left:

42-(d^2-22d)=0

We get rid of parentheses

-d^2+22d+42=0

We add all the numbers together, and all the variables

-1d^2+22d+42=0

a = -1; b = 22; c = +42;
Δ = b2-4ac
Δ = 222-4·(-1)·42
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{163}}{2*-1}=\frac{-22-2\sqrt{163}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{163}}{2*-1}=\frac{-22+2\sqrt{163}}{-2}
$