10+(5/x)+(3/3x)=11

Solution for 10+(5/x)+(3/3x)=11 equation:

10+(5/x)+(3/3x)=11

We move all terms to the left:

10+(5/x)+(3/3x)-(11)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/x)+(+3/3x)+10-11=0

We add all the numbers together, and all the variables

(+5/x)+(+3/3x)-1=0

We get rid of parentheses

5/x+3/3x-1=0

We calculate fractions


15x/3x^2+3x/3x^2-1=0

We multiply all the terms by the denominator


15x+3x-1*3x^2=0

We add all the numbers together, and all the variables

18x-1*3x^2=0

Wy multiply elements

-3x^2+18x=0

a = -3; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-3)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-3}=\frac{0}{-6}
=0
$