x-6/x=-11

Solution for x-6/x=-11 equation:

x-6/x=-11

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-6/x+11=0

We multiply all the terms by the denominator


x*x+11*x-6=0

We add all the numbers together, and all the variables

11x+x*x-6=0

Wy multiply elements

x^2+11x-6=0

a = 1; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·1·(-6)
Δ = 145
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{145}}{2*1}=\frac{-11-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{145}}{2*1}=\frac{-11+\sqrt{145}}{2}
$