4/x+4=16x=

Solution for 4/x+4=16x= equation:

4/x+4=16x=

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-16x+4/x+4=0

We multiply all the terms by the denominator


-16x*x+4*x+4=0

We add all the numbers together, and all the variables

4x-16x*x+4=0

Wy multiply elements

-16x^2+4x+4=0

a = -16; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-16)·4
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{17}}{2*-16}=\frac{-4-4\sqrt{17}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{17}}{2*-16}=\frac{-4+4\sqrt{17}}{-32}
$