364=x*(1/2x+1)

Solution for 364=x*(1/2x+1) equation:

364=x(1/2x+1)

We move all terms to the left:

364-(x(1/2x+1))=0


Domain of the equation: 2x+1))!=0

x∈R


We multiply all the terms by the denominator


-(x(1+364*2x+1))=0


We calculate terms in parentheses: -(x(1+364*2x+1)), so:

x(1+364*2x+1)

We add all the numbers together, and all the variables

x(364*2x+2)

We multiply parentheses

728x^2+2x

Back to the equation:

-(728x^2+2x)


We get rid of parentheses

-728x^2-2x=0

a = -728; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-728)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-728}=\frac{0}{-1456}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-728}=\frac{4}{-1456}
=-1/364
$