5/x+2=12x

Solution for 5/x+2=12x equation:

5/x+2=12x

We move all terms to the left:

5/x+2-(12x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-12x+5/x+2=0

We multiply all the terms by the denominator


-12x*x+2*x+5=0

We add all the numbers together, and all the variables

2x-12x*x+5=0

Wy multiply elements

-12x^2+2x+5=0

a = -12; b = 2; c = +5;
Δ = b2-4ac
Δ = 22-4·(-12)·5
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*-12}=\frac{-2-2\sqrt{61}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*-12}=\frac{-2+2\sqrt{61}}{-24}
$