3x+11/x=21.5

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Solution for 3x+11/x=21.5 equation: 



3x+11/x=21.5

We move all terms to the left:

3x+11/x-(21.5)=0



Domain of the equation: x!=0

x∈R



We add all the numbers together, and all the variables

3x+11/x-21.5=0

We multiply all the terms by the denominator


3x*x-(21.5)*x+11=0

We multiply parentheses

3x*x-21.5x+11=0

Wy multiply elements

3x^2-21.5x+11=0

a = 3; b = -21.5; c = +11;
Δ = b2-4ac
Δ = -21.52-4·3·11
Δ = 330.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21.5)-\sqrt{330.25}}{2*3}=\frac{21.5-\sqrt{330.25}}{6}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21.5)+\sqrt{330.25}}{2*3}=\frac{21.5+\sqrt{330.25}}{6}
$

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