3/x+3=7/5x+6

Solution for 3/x+3=7/5x+6 equation:

3/x+3=7/5x+6

We move all terms to the left:

3/x+3-(7/5x+6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+6)!=0

x∈R


We get rid of parentheses

3/x-7/5x-6+3=0

We calculate fractions


15x/5x^2+(-7x)/5x^2-6+3=0

We add all the numbers together, and all the variables

15x/5x^2+(-7x)/5x^2-3=0

We multiply all the terms by the denominator


15x+(-7x)-3*5x^2=0

Wy multiply elements

-15x^2+15x+(-7x)=0

We get rid of parentheses

-15x^2+15x-7x=0

We add all the numbers together, and all the variables

-15x^2+8x=0

a = -15; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-15)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-15}=\frac{-16}{-30}
=8/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-15}=\frac{0}{-30}
=0
$