200=1/2(4x^2)

Solution for 200=1/2(4x^2) equation:

200=1/2(4x^2)

We move all terms to the left:

200-(1/2(4x^2))=0


Domain of the equation: 24x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/24x^2+200=0

We multiply all the terms by the denominator


200*24x^2-1=0

Wy multiply elements

4800x^2-1=0

a = 4800; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·4800·(-1)
Δ = 19200
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:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{3}}{2*4800}=\frac{0-80\sqrt{3}}{9600}
=-\frac{80\sqrt{3}}{9600}
=-\frac{\sqrt{3}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{3}}{2*4800}=\frac{0+80\sqrt{3}}{9600}
=\frac{80\sqrt{3}}{9600}
=\frac{\sqrt{3}}{120}
$