x-3/3=11/x+5

Solution for x-3/3=11/x+5 equation:

x-3/3=11/x+5

We move all terms to the left:

x-3/3-(11/x+5)=0


Domain of the equation: x+5)!=0

x∈R


We add all the numbers together, and all the variables

x-(11/x+5)-1=0

We get rid of parentheses

x-11/x-5-1=0

We multiply all the terms by the denominator


x*x-5*x-1*x-11=0

We add all the numbers together, and all the variables

-6x+x*x-11=0

Wy multiply elements

x^2-6x-11=0

a = 1; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·1·(-11)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{5}}{2*1}=\frac{6-4\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{5}}{2*1}=\frac{6+4\sqrt{5}}{2}
$