5/3x+53=6/5x+39

Solution for 5/3x+53=6/5x+39 equation:

5/3x+53=6/5x+39

We move all terms to the left:

5/3x+53-(6/5x+39)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+39)!=0

x∈R


We get rid of parentheses

5/3x-6/5x-39+53=0

We calculate fractions


25x/15x^2+(-18x)/15x^2-39+53=0

We add all the numbers together, and all the variables

25x/15x^2+(-18x)/15x^2+14=0

We multiply all the terms by the denominator


25x+(-18x)+14*15x^2=0

Wy multiply elements

210x^2+25x+(-18x)=0

We get rid of parentheses

210x^2+25x-18x=0

We add all the numbers together, and all the variables

210x^2+7x=0

a = 210; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·210·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*210}=\frac{-14}{420}
=-1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*210}=\frac{0}{420}
=0
$