42=d^2-22

Solution for 42=d^2-22 equation:

42=d^2-22

We move all terms to the left:

42-(d^2-22)=0

We get rid of parentheses

-d^2+22+42=0

We add all the numbers together, and all the variables

-1d^2+64=0

a = -1; b = 0; c = +64;
Δ = b2-4ac
Δ = 02-4·(-1)·64
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*-1}=\frac{-16}{-2}
=+8
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*-1}=\frac{16}{-2}
=-8
$