11x-3/x=2

Solution for 11x-3/x=2 equation:

11x-3/x=2

We move all terms to the left:

11x-3/x-(2)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


11x*x-2*x-3=0

We add all the numbers together, and all the variables

-2x+11x*x-3=0

Wy multiply elements

11x^2-2x-3=0

a = 11; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·11·(-3)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{34}}{2*11}=\frac{2-2\sqrt{34}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{34}}{2*11}=\frac{2+2\sqrt{34}}{22}
$