3/4x^2=-1/4x^2+4

Solution for 3/4x^2=-1/4x^2+4 equation:

3/4x^2=-1/4x^2+4

We move all terms to the left:

3/4x^2-(-1/4x^2+4)=0


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

x^2!=0/4

x^2!=√0

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/4x^2+1/4x^2-4=0

We multiply all the terms by the denominator


-4*4x^2+3+1=0

We add all the numbers together, and all the variables

-4*4x^2+4=0

Wy multiply elements

-16x^2+4=0

a = -16; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-16)·4
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*-16}=\frac{-16}{-32}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*-16}=\frac{16}{-32}
=-1/2
$