1/4x^+x-2=0

Solution for 1/4x^+x-2=0 equation:

1/4x^+x-2=0


Domain of the equation: 4x^!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/4x^-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-8x+1=0

a = 4; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·4·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*4}=\frac{8-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*4}=\frac{8+4\sqrt{3}}{8}
$