3/6x=5/5x+2

Solution for 3/6x=5/5x+2 equation:

3/6x=5/5x+2

We move all terms to the left:

3/6x-(5/5x+2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

3/6x-5/5x-2=0

We calculate fractions


15x/30x^2+(-30x)/30x^2-2=0

We multiply all the terms by the denominator


15x+(-30x)-2*30x^2=0

Wy multiply elements

-60x^2+15x+(-30x)=0

We get rid of parentheses

-60x^2+15x-30x=0

We add all the numbers together, and all the variables

-60x^2-15x=0

a = -60; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-60)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-60}=\frac{30}{-120}
=-1/4
$