5x-2-6/x=0

Solution for 5x-2-6/x=0 equation:

5x-2-6/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-2x-6=0

a = 5; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·5·(-6)
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{-(-2)-2\sqrt{31}}{2*5}=\frac{2-2\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*5}=\frac{2+2\sqrt{31}}{10}
$