d^2=26/144

Solution for d^2=26/144 equation:

d^2=26/144

We move all terms to the left:

d^2-(26/144)=0

We add all the numbers together, and all the variables

d^2-(+26/144)=0

We get rid of parentheses

d^2-26/144=0

We multiply all the terms by the denominator


d^2*144-26=0

Wy multiply elements

144d^2-26=0

a = 144; b = 0; c = -26;
Δ = b2-4ac
Δ = 02-4·144·(-26)
Δ = 14976
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:

$\sqrt{\Delta}=\sqrt{14976}=\sqrt{576*26}=\sqrt{576}*\sqrt{26}=24\sqrt{26}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{26}}{2*144}=\frac{0-24\sqrt{26}}{288}
=-\frac{24\sqrt{26}}{288}
=-\frac{\sqrt{26}}{12}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{26}}{2*144}=\frac{0+24\sqrt{26}}{288}
=\frac{24\sqrt{26}}{288}
=\frac{\sqrt{26}}{12}
$