4/x=1.618*x

Solution for 4/x=1.618*x equation:

4/x=1.618x

We move all terms to the left:

4/x-(1.618x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4/x-(+1.618x)=0

We get rid of parentheses

4/x-1.618x=0

We multiply all the terms by the denominator


-(1.618x)*x+4=0

We add all the numbers together, and all the variables

-(+1.618x)*x+4=0

We multiply parentheses

-x^2+4=0

We add all the numbers together, and all the variables

-1x^2+4=0

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

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