(2/x)-5=4x+2

Solution for (2/x)-5=4x+2 equation:

(2/x)-5=4x+2

We move all terms to the left:

(2/x)-5-(4x+2)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/x)-(4x+2)-5=0

We get rid of parentheses

2/x-4x-2-5=0

We multiply all the terms by the denominator


-4x*x-2*x-5*x+2=0

We add all the numbers together, and all the variables

-7x-4x*x+2=0

Wy multiply elements

-4x^2-7x+2=0

a = -4; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-4)·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-4}=\frac{16}{-8}
=-2
$