1/4x^2=400

Solution for 1/4x^2=400 equation:

1/4x^2=400

We move all terms to the left:

1/4x^2-(400)=0


Domain of the equation: 4x^2!=0

x^2!=0/4

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-400*4x^2+1=0

Wy multiply elements

-1600x^2+1=0

a = -1600; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1600)·1
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*-1600}=\frac{-80}{-3200}
=1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*-1600}=\frac{80}{-3200}
=-1/40
$