4x+12=11/x

Solution for 4x+12=11/x equation:

4x+12=11/x

We move all terms to the left:

4x+12-(11/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

4x-(+11/x)+12=0

We get rid of parentheses

4x-11/x+12=0

We multiply all the terms by the denominator


4x*x+12*x-11=0

We add all the numbers together, and all the variables

12x+4x*x-11=0

Wy multiply elements

4x^2+12x-11=0

a = 4; b = 12; c = -11;
Δ = b2-4ac
Δ = 122-4·4·(-11)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{5}}{2*4}=\frac{-12-8\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{5}}{2*4}=\frac{-12+8\sqrt{5}}{8}
$