5/5x=6/3x+4

Solution for 5/5x=6/3x+4 equation:

5/5x=6/3x+4

We move all terms to the left:

5/5x-(6/3x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

5/5x-6/3x-4=0

We calculate fractions


15x/15x^2+(-30x)/15x^2-4=0

We multiply all the terms by the denominator


15x+(-30x)-4*15x^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
$