1/48x+16=4x

Solution for 1/48x+16=4x equation:

1/48x+16=4x

We move all terms to the left:

1/48x+16-(4x)=0


Domain of the equation: 48x!=0

x!=0/48

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+1/48x+16=0

We multiply all the terms by the denominator


-4x*48x+16*48x+1=0

Wy multiply elements

-192x^2+768x+1=0

a = -192; b = 768; c = +1;
Δ = b2-4ac
Δ = 7682-4·(-192)·1
Δ = 590592
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:

$\sqrt{\Delta}=\sqrt{590592}=\sqrt{256*2307}=\sqrt{256}*\sqrt{2307}=16\sqrt{2307}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(768)-16\sqrt{2307}}{2*-192}=\frac{-768-16\sqrt{2307}}{-384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(768)+16\sqrt{2307}}{2*-192}=\frac{-768+16\sqrt{2307}}{-384}
$