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

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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
-3x-4x*x+2=0
Wy multiply elements
-4x^2-3x+2=0
a = -4; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-4)·2
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{41}}{2*-4}=\frac{3-\sqrt{41}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*-4}=\frac{3+\sqrt{41}}{-8} $

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