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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

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

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

We get rid of parentheses

2x/4x+2/2x-5/6=0

We calculate fractions


(-80x^2)/288x^2+144x^2/288x^2+288x/288x^2=0

We multiply all the terms by the denominator


(-80x^2)+144x^2+288x=0

We add all the numbers together, and all the variables

144x^2+(-80x^2)+288x=0

We get rid of parentheses

144x^2-80x^2+288x=0

We add all the numbers together, and all the variables

64x^2+288x=0

a = 64; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·64·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*64}=\frac{-576}{128}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*64}=\frac{0}{128}
=0
$