2/x-6=5x

Solution for 2/x-6=5x equation:

2/x-6=5x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+2/x-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -5; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-5)·2
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*-5}=\frac{6-2\sqrt{19}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*-5}=\frac{6+2\sqrt{19}}{-10}
$