x=7/x-11

Solution for x=7/x-11 equation:

x=7/x-11

We move all terms to the left:

x-(7/x-11)=0


Domain of the equation: x-11)!=0

x∈R


We get rid of parentheses

x-7/x+11=0

We multiply all the terms by the denominator


x*x+11*x-7=0

We add all the numbers together, and all the variables

11x+x*x-7=0

Wy multiply elements

x^2+11x-7=0

a = 1; b = 11; c = -7;
Δ = b2-4ac
Δ = 112-4·1·(-7)
Δ = 149
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{-(11)-\sqrt{149}}{2*1}=\frac{-11-\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{149}}{2*1}=\frac{-11+\sqrt{149}}{2}
$