4x+2/x=92

Solution for 4x+2/x=92 equation:

4x+2/x=92

We move all terms to the left:

4x+2/x-(92)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-92*x+2=0

We add all the numbers together, and all the variables

-92x+4x*x+2=0

Wy multiply elements

4x^2-92x+2=0

a = 4; b = -92; c = +2;
Δ = b2-4ac
Δ = -922-4·4·2
Δ = 8432
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:

$\sqrt{\Delta}=\sqrt{8432}=\sqrt{16*527}=\sqrt{16}*\sqrt{527}=4\sqrt{527}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{527}}{2*4}=\frac{92-4\sqrt{527}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{527}}{2*4}=\frac{92+4\sqrt{527}}{8}
$