x+6/x=5x+12/6

Solution for x+6/x=5x+12/6 equation:

x+6/x=5x+12/6

We move all terms to the left:

x+6/x-(5x+12/6)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+6/x-(5x+2)=0

We get rid of parentheses

x+6/x-5x-2=0

We multiply all the terms by the denominator


x*x-5x*x-2*x+6=0

We add all the numbers together, and all the variables

-2x+x*x-5x*x+6=0

Wy multiply elements

x^2-5x^2-2x+6=0

We add all the numbers together, and all the variables

-4x^2-2x+6=0

a = -4; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-4)·6
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-4}=\frac{12}{-8}
=-1+1/2
$