1/x-2+1/2x-4=5/6

Solution for 1/x-2+1/2x-4=5/6 equation:

1/x-2+1/2x-4=5/6

We move all terms to the left:

1/x-2+1/2x-4-(5/6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+1/2x-2-4-(+5/6)=0

We add all the numbers together, and all the variables

1/x+1/2x-6-(+5/6)=0

We get rid of parentheses

1/x+1/2x-6-5/6=0

We calculate fractions


(-20x^2)/72x^2+72x/72x^2+36x/72x^2-6=0

We multiply all the terms by the denominator


(-20x^2)+72x+36x-6*72x^2=0

We add all the numbers together, and all the variables

(-20x^2)+108x-6*72x^2=0

Wy multiply elements

(-20x^2)-432x^2+108x=0

We get rid of parentheses

-20x^2-432x^2+108x=0

We add all the numbers together, and all the variables

-452x^2+108x=0

a = -452; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-452)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-452}=\frac{-216}{-904}
=27/113
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-452}=\frac{0}{-904}
=0
$