4x=180,5/x+2x

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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 $

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