10x+11=6/x

Solution for 10x+11=6/x equation:

10x+11=6/x

We move all terms to the left:

10x+11-(6/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

10x-(+6/x)+11=0

We get rid of parentheses

10x-6/x+11=0

We multiply all the terms by the denominator


10x*x+11*x-6=0

We add all the numbers together, and all the variables

11x+10x*x-6=0

Wy multiply elements

10x^2+11x-6=0

a = 10; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·10·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*10}=\frac{-30}{20}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*10}=\frac{8}{20}
=2/5
$