7/x+9=-32/15x-2

Solution for 7/x+9=-32/15x-2 equation:

7/x+9=-32/15x-2

We move all terms to the left:

7/x+9-(-32/15x-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 15x-2)!=0

x∈R


We get rid of parentheses

7/x+32/15x+2+9=0

We calculate fractions


105x/15x^2+32x/15x^2+2+9=0

We add all the numbers together, and all the variables

105x/15x^2+32x/15x^2+11=0

We multiply all the terms by the denominator


105x+32x+11*15x^2=0

We add all the numbers together, and all the variables

137x+11*15x^2=0

Wy multiply elements

165x^2+137x=0

a = 165; b = 137; c = 0;
Δ = b2-4ac
Δ = 1372-4·165·0
Δ = 18769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18769}=137$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(137)-137}{2*165}=\frac{-274}{330}
=-137/165
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(137)+137}{2*165}=\frac{0}{330}
=0
$