1/3x-2=16x+5

Solution for 1/3x-2=16x+5 equation:

1/3x-2=16x+5

We move all terms to the left:

1/3x-2-(16x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-16x-5-2=0

We multiply all the terms by the denominator


-16x*3x-5*3x-2*3x+1=0

Wy multiply elements

-48x^2-15x-6x+1=0

We add all the numbers together, and all the variables

-48x^2-21x+1=0

a = -48; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·(-48)·1
Δ = 633
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{633}}{2*-48}=\frac{21-\sqrt{633}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{633}}{2*-48}=\frac{21+\sqrt{633}}{-96}
$