7-x=11/x

Solution for 7-x=11/x equation:

7-x=11/x

We move all terms to the left:

7-x-(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

-x-(+11/x)+7=0

We add all the numbers together, and all the variables

-1x-(+11/x)+7=0

We get rid of parentheses

-1x-11/x+7=0

We multiply all the terms by the denominator


-1x*x+7*x-11=0

We add all the numbers together, and all the variables

7x-1x*x-11=0

Wy multiply elements

-1x^2+7x-11=0

a = -1; b = 7; c = -11;
Δ = b2-4ac
Δ = 72-4·(-1)·(-11)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{5}}{2*-1}=\frac{-7-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{5}}{2*-1}=\frac{-7+\sqrt{5}}{-2}
$