196=1/2x^2

Solution for 196=1/2x^2 equation:

196=1/2x^2

We move all terms to the left:

196-(1/2x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/2x^2+196=0

We multiply all the terms by the denominator


196*2x^2-1=0

Wy multiply elements

392x^2-1=0

a = 392; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·392·(-1)
Δ = 1568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*392}=\frac{0-28\sqrt{2}}{784}
=-\frac{28\sqrt{2}}{784}
=-\frac{\sqrt{2}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*392}=\frac{0+28\sqrt{2}}{784}
=\frac{28\sqrt{2}}{784}
=\frac{\sqrt{2}}{28}
$