12x+5=1/12x

Solution for 12x+5=1/12x equation:

12x+5=1/12x

We move all terms to the left:

12x+5-(1/12x)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12x-(+1/12x)+5=0

We get rid of parentheses

12x-1/12x+5=0

We multiply all the terms by the denominator


12x*12x+5*12x-1=0

Wy multiply elements

144x^2+60x-1=0

a = 144; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·144·(-1)
Δ = 4176
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:

$\sqrt{\Delta}=\sqrt{4176}=\sqrt{144*29}=\sqrt{144}*\sqrt{29}=12\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{29}}{2*144}=\frac{-60-12\sqrt{29}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{29}}{2*144}=\frac{-60+12\sqrt{29}}{288}
$