4x-12/x=11

Solution for 4x-12/x=11 equation:

4x-12/x=11

We move all terms to the left:

4x-12/x-(11)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-11*x-12=0

We add all the numbers together, and all the variables

-11x+4x*x-12=0

Wy multiply elements

4x^2-11x-12=0

a = 4; b = -11; c = -12;
Δ = b2-4ac
Δ = -112-4·4·(-12)
Δ = 313
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{313}}{2*4}=\frac{11-\sqrt{313}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{313}}{2*4}=\frac{11+\sqrt{313}}{8}
$