16x+2=1/24x

Solution for 16x+2=1/24x equation:

16x+2=1/24x

We move all terms to the left:

16x+2-(1/24x)=0


Domain of the equation: 24x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

16x-(+1/24x)+2=0

We get rid of parentheses

16x-1/24x+2=0

We multiply all the terms by the denominator


16x*24x+2*24x-1=0

Wy multiply elements

384x^2+48x-1=0

a = 384; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·384·(-1)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{15}}{2*384}=\frac{-48-16\sqrt{15}}{768}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{15}}{2*384}=\frac{-48+16\sqrt{15}}{768}
$