3x-4+4/x=22

Solution for 3x-4+4/x=22 equation:

3x-4+4/x=22

We move all terms to the left:

3x-4+4/x-(22)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+4/x-26=0

We multiply all the terms by the denominator


3x*x-26*x+4=0

We add all the numbers together, and all the variables

-26x+3x*x+4=0

Wy multiply elements

3x^2-26x+4=0

a = 3; b = -26; c = +4;
Δ = b2-4ac
Δ = -262-4·3·4
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{157}}{2*3}=\frac{26-2\sqrt{157}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{157}}{2*3}=\frac{26+2\sqrt{157}}{6}
$