(16x^2-6)/(4x^2-1)=0

Solution for (16x^2-6)/(4x^2-1)=0 equation:

(16x^2-6)/(4x^2-1)=0


Domain of the equation: (4x^2-1)!=0

We move all terms containing x to the left, all other terms to the right

4x^2!=1

x^2!=1/4

x^2!=√1/4

x!=1

x∈R


We multiply all the terms by the denominator


(16x^2-6)=0

We get rid of parentheses

16x^2-6=0

a = 16; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·16·(-6)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*16}=\frac{0-8\sqrt{6}}{32}
=-\frac{8\sqrt{6}}{32}
=-\frac{\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*16}=\frac{0+8\sqrt{6}}{32}
=\frac{8\sqrt{6}}{32}
=\frac{\sqrt{6}}{4}
$