9/x-3=7x-5

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

9/x-3=7x-5

We move all terms to the left:

9/x-3-(7x-5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-7x*x+5*x-3*x+9=0

We add all the numbers together, and all the variables

2x-7x*x+9=0

Wy multiply elements

-7x^2+2x+9=0

a = -7; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-7)·9
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*-7}=\frac{-18}{-14}
=1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*-7}=\frac{14}{-14}
=-1
$