2x+12=110/x

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
$