5x/3x+7=4x/5

Solution for 5x/3x+7=4x/5 equation:

5x/3x+7=4x/5

We move all terms to the left:

5x/3x+7-(4x/5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x/3x-(+4x/5)+7=0

We get rid of parentheses

5x/3x-4x/5+7=0

We calculate fractions


(-12x^2)/15x+25x/15x+7=0

We multiply all the terms by the denominator


(-12x^2)+25x+7*15x=0

Wy multiply elements

(-12x^2)+25x+105x=0

We get rid of parentheses

-12x^2+25x+105x=0

We add all the numbers together, and all the variables

-12x^2+130x=0

a = -12; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·(-12)·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*-12}=\frac{-260}{-24}
=10+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*-12}=\frac{0}{-24}
=0
$