11x-4/x=2

Solution for 11x-4/x=2 equation:

11x-4/x=2

We move all terms to the left:

11x-4/x-(2)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


11x*x-2*x-4=0

We add all the numbers together, and all the variables

-2x+11x*x-4=0

Wy multiply elements

11x^2-2x-4=0

a = 11; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·11·(-4)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{5}}{2*11}=\frac{2-6\sqrt{5}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{5}}{2*11}=\frac{2+6\sqrt{5}}{22}
$