507=7.5/d^2

Solution for 507=7.5/d^2 equation:

507=7.5/d^2

We move all terms to the left:

507-(7.5/d^2)=0


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

d!=0/1

d!=0

d∈R


We get rid of parentheses

-7.5/d^2+507=0

We multiply all the terms by the denominator


507*d^2-7.5=0

We add all the numbers together, and all the variables

507d^2-7.5=0

a = 507; b = 0; c = -7.5;
Δ = b2-4ac
Δ = 02-4·507·(-7.5)
Δ = 15210
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:

$\sqrt{\Delta}=\sqrt{15210}=\sqrt{1521*10}=\sqrt{1521}*\sqrt{10}=39\sqrt{10}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-39\sqrt{10}}{2*507}=\frac{0-39\sqrt{10}}{1014}
=-\frac{39\sqrt{10}}{1014}
=-\frac{\sqrt{10}}{26}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+39\sqrt{10}}{2*507}=\frac{0+39\sqrt{10}}{1014}
=\frac{39\sqrt{10}}{1014}
=\frac{\sqrt{10}}{26}
$