6/x-7+9/5x-35=-3

Solution for 6/x-7+9/5x-35=-3 equation:

6/x-7+9/5x-35=-3

We move all terms to the left:

6/x-7+9/5x-35-(-3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

6/x+9/5x-39=0

We calculate fractions


30x/5x^2+9x/5x^2-39=0

We multiply all the terms by the denominator


30x+9x-39*5x^2=0

We add all the numbers together, and all the variables

39x-39*5x^2=0

Wy multiply elements

-195x^2+39x=0

a = -195; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-195)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-195}=\frac{-78}{-390}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-195}=\frac{0}{-390}
=0
$