1/2d^2=13

Solution for 1/2d^2=13 equation:

1/2d^2=13

We move all terms to the left:

1/2d^2-(13)=0


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

d^2!=0/2

d^2!=√0

d!=0

d∈R


We multiply all the terms by the denominator


-13*2d^2+1=0

Wy multiply elements

-26d^2+1=0

a = -26; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-26)·1
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*-26}=\frac{0-2\sqrt{26}}{-52}
=-\frac{2\sqrt{26}}{-52}
=-\frac{\sqrt{26}}{-26}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*-26}=\frac{0+2\sqrt{26}}{-52}
=\frac{2\sqrt{26}}{-52}
=\frac{\sqrt{26}}{-26}
$