x+41/2x=44,00

Solution for x+41/2x=44,00 equation:

x+41/2x=44.00

We move all terms to the left:

x+41/2x-(44.00)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+41/2x-44=0

We multiply all the terms by the denominator


x*2x-44*2x+41=0

Wy multiply elements

2x^2-88x+41=0

a = 2; b = -88; c = +41;
Δ = b2-4ac
Δ = -882-4·2·41
Δ = 7416
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:

$\sqrt{\Delta}=\sqrt{7416}=\sqrt{36*206}=\sqrt{36}*\sqrt{206}=6\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-6\sqrt{206}}{2*2}=\frac{88-6\sqrt{206}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+6\sqrt{206}}{2*2}=\frac{88+6\sqrt{206}}{4}
$