9x-10/x+13=0

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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 $

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