2x+12=110/x

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Solution for 2x+12=110/x equation:



2x+12=110/x
We move all terms to the left:
2x+12-(110/x)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2x-(+110/x)+12=0
We get rid of parentheses
2x-110/x+12=0
We multiply all the terms by the denominator
2x*x+12*x-110=0
We add all the numbers together, and all the variables
12x+2x*x-110=0
Wy multiply elements
2x^2+12x-110=0
a = 2; b = 12; c = -110;
Δ = b2-4ac
Δ = 122-4·2·(-110)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-32}{2*2}=\frac{-44}{4} =-11 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+32}{2*2}=\frac{20}{4} =5 $

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