11/x+8=x+3/x+20

Solution for 11/x+8=x+3/x+20 equation:

11/x+8=x+3/x+20

We move all terms to the left:

11/x+8-(x+3/x+20)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+20)!=0

x∈R


We get rid of parentheses

11/x-x-3/x-20+8=0

We multiply all the terms by the denominator


-x*x-20*x+8*x+11-3=0

We add all the numbers together, and all the variables

-12x-x*x+8=0

Wy multiply elements

-1x^2-12x+8=0

a = -1; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·(-1)·8
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{11}}{2*-1}=\frac{12-4\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{11}}{2*-1}=\frac{12+4\sqrt{11}}{-2}
$