2x+-1/4x=3

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

2x+-1/4x=3

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


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

We add all the numbers together, and all the variables

2x-1/4x=0

We multiply all the terms by the denominator


2x*4x-1=0

Wy multiply elements

8x^2-1=0

a = 8; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8·(-1)
Δ = 32
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:

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