1=2560/d^2

Solution for 1=2560/d^2 equation:

1=2560/d^2

We move all terms to the left:

1-(2560/d^2)=0


Domain of the equation: d^2)!=0

d!=0/1

d!=0

d∈R


We get rid of parentheses

-2560/d^2+1=0

We multiply all the terms by the denominator


1*d^2-2560=0

We add all the numbers together, and all the variables

d^2-2560=0

a = 1; b = 0; c = -2560;
Δ = b2-4ac
Δ = 02-4·1·(-2560)
Δ = 10240
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:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{10}}{2*1}=\frac{0-32\sqrt{10}}{2}
=-\frac{32\sqrt{10}}{2}
=-16\sqrt{10}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{10}}{2*1}=\frac{0+32\sqrt{10}}{2}
=\frac{32\sqrt{10}}{2}
=16\sqrt{10}
$