4x-1/x+3=4

Solution for 4x-1/x+3=4 equation:

4x-1/x+3=4

We move all terms to the left:

4x-1/x+3-(4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-1/x-1=0

We multiply all the terms by the denominator


4x*x-1*x-1=0

We add all the numbers together, and all the variables

-1x+4x*x-1=0

Wy multiply elements

4x^2-1x-1=0

a = 4; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·4·(-1)
Δ = 17
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{-(-1)-\sqrt{17}}{2*4}=\frac{1-\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*4}=\frac{1+\sqrt{17}}{8}
$