X=1/618x+4=

Solution for X=1/618x+4= equation:

X=1/618X+4=

We move all terms to the left:

X-(1/618X+4)=0


Domain of the equation: 618X+4)!=0

X∈R


We get rid of parentheses

X-1/618X-4=0

We multiply all the terms by the denominator


X*618X-4*618X-1=0

Wy multiply elements

618X^2-2472X-1=0

a = 618; b = -2472; c = -1;
Δ = b2-4ac
Δ = -24722-4·618·(-1)
Δ = 6113256
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:

$\sqrt{\Delta}=\sqrt{6113256}=\sqrt{4*1528314}=\sqrt{4}*\sqrt{1528314}=2\sqrt{1528314}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2472)-2\sqrt{1528314}}{2*618}=\frac{2472-2\sqrt{1528314}}{1236}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2472)+2\sqrt{1528314}}{2*618}=\frac{2472+2\sqrt{1528314}}{1236}
$