5/x-6=3x+2

Solution for 5/x-6=3x+2 equation:

5/x-6=3x+2

We move all terms to the left:

5/x-6-(3x+2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5/x-3x-2-6=0

We multiply all the terms by the denominator


-3x*x-2*x-6*x+5=0

We add all the numbers together, and all the variables

-8x-3x*x+5=0

Wy multiply elements

-3x^2-8x+5=0

a = -3; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·(-3)·5
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{31}}{2*-3}=\frac{8-2\sqrt{31}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{31}}{2*-3}=\frac{8+2\sqrt{31}}{-6}
$