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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-30x)/12x^2+(-2x)/12x^2+2=0

We multiply all the terms by the denominator


(-30x)+(-2x)+2*12x^2=0

Wy multiply elements

24x^2+(-30x)+(-2x)=0

We get rid of parentheses

24x^2-30x-2x=0

We add all the numbers together, and all the variables

24x^2-32x=0

a = 24; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·24·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*24}=\frac{64}{48}
=1+1/3
$