11x-4/x=3

Solution for 11x-4/x=3 equation:

11x-4/x=3

We move all terms to the left:

11x-4/x-(3)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


11x*x-3*x-4=0

We add all the numbers together, and all the variables

-3x+11x*x-4=0

Wy multiply elements

11x^2-3x-4=0

a = 11; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·11·(-4)
Δ = 185
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{-(-3)-\sqrt{185}}{2*11}=\frac{3-\sqrt{185}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{185}}{2*11}=\frac{3+\sqrt{185}}{22}
$