9x-10/x+13=0

Solution for 9x-10/x+13=0 equation:

9x-10/x+13=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


9x*x+13*x-10=0

We add all the numbers together, and all the variables

13x+9x*x-10=0

Wy multiply elements

9x^2+13x-10=0

a = 9; b = 13; c = -10;
Δ = b2-4ac
Δ = 132-4·9·(-10)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*9}=\frac{-36}{18}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*9}=\frac{10}{18}
=5/9
$