42-d2=22

Solution for 42-d2=22 equation:

42-d2=22

We move all terms to the left:

42-d2-(22)=0

We add all the numbers together, and all the variables

-1d^2+20=0

a = -1; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-1)·20
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*-1}=\frac{0-4\sqrt{5}}{-2}
=-\frac{4\sqrt{5}}{-2}
=-\frac{2\sqrt{5}}{-1}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*-1}=\frac{0+4\sqrt{5}}{-2}
=\frac{4\sqrt{5}}{-2}
=\frac{2\sqrt{5}}{-1}
$