(x*1.618)*x=4

Solution for (x*1.618)*x=4 equation:

(x*1.618)*x=4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

1.618x^2-4=0

a = 1.618; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1.618·(-4)
Δ = 25.888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{25.888}}{2*1.618}=\frac{0-\sqrt{25.888}}{3.236}
=-\frac{\sqrt{}}{3.236}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{25.888}}{2*1.618}=\frac{0+\sqrt{25.888}}{3.236}
=\frac{\sqrt{}}{3.236}
$