1/2a2^2=52

Solution for 1/2a2^2=52 equation:

1/2a^2^2=52

We move all terms to the left:

1/2a^2^2-(52)=0


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

a!=0/1

a!=0

a∈R


We multiply all the terms by the denominator


-52*2a^2^2+1=0

Wy multiply elements

-104a^2+1=0

a = -104; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-104)·1
Δ = 416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*-104}=\frac{0-4\sqrt{26}}{-208}
=-\frac{4\sqrt{26}}{-208}
=-\frac{\sqrt{26}}{-52}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*-104}=\frac{0+4\sqrt{26}}{-208}
=\frac{4\sqrt{26}}{-208}
=\frac{\sqrt{26}}{-52}
$