1/2x^2=648

Solution for 1/2x^2=648 equation:

1/2x^2=648

We move all terms to the left:

1/2x^2-(648)=0


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

x^2!=0/2

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-648*2x^2+1=0

Wy multiply elements

-1296x^2+1=0

a = -1296; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1296)·1
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*-1296}=\frac{-72}{-2592}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*-1296}=\frac{72}{-2592}
=-1/36
$