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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


30x/12x^2+(-10x)/12x^2+4+1=0

We add all the numbers together, and all the variables

30x/12x^2+(-10x)/12x^2+5=0

We multiply all the terms by the denominator


30x+(-10x)+5*12x^2=0

Wy multiply elements

60x^2+30x+(-10x)=0

We get rid of parentheses

60x^2+30x-10x=0

We add all the numbers together, and all the variables

60x^2+20x=0

a = 60; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·60·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*60}=\frac{-40}{120}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*60}=\frac{0}{120}
=0
$