4/x=16(5x)+4

Solution for 4/x=16(5x)+4 equation:

4/x=16(5x)+4

We move all terms to the left:

4/x-(16(5x)+4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-165x-4=0

We multiply all the terms by the denominator


-165x*x-4*x+4=0

We add all the numbers together, and all the variables

-4x-165x*x+4=0

Wy multiply elements

-165x^2-4x+4=0

a = -165; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-165)·4
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{166}}{2*-165}=\frac{4-4\sqrt{166}}{-330}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{166}}{2*-165}=\frac{4+4\sqrt{166}}{-330}
$