4x=180.5/x+2x

Solution for 4x=180.5/x+2x equation:

4x=180.5/x+2x

We move all terms to the left:

4x-(180.5/x+2x)=0


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

x∈R


We add all the numbers together, and all the variables

4x-(+2x+180.5/x)=0

We get rid of parentheses

4x-2x-180.5/x=0

We multiply all the terms by the denominator


4x*x-2x*x-180.5=0

Wy multiply elements

4x^2-2x^2-180.5=0

We add all the numbers together, and all the variables

2x^2-180.5=0

a = 2; b = 0; c = -180.5;
Δ = b2-4ac
Δ = 02-4·2·(-180.5)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-38}{2*2}=\frac{-38}{4}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+38}{2*2}=\frac{38}{4}
=9+1/2
$