x+9/9=3/x-8

Solution for x+9/9=3/x-8 equation:

x+9/9=3/x-8

We move all terms to the left:

x+9/9-(3/x-8)=0


Domain of the equation: x-8)!=0

x∈R


We add all the numbers together, and all the variables

x-(3/x-8)+1=0

We get rid of parentheses

x-3/x+8+1=0

We multiply all the terms by the denominator


x*x+8*x+1*x-3=0

We add all the numbers together, and all the variables

9x+x*x-3=0

Wy multiply elements

x^2+9x-3=0

a = 1; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·1·(-3)
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{93}}{2*1}=\frac{-9-\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{93}}{2*1}=\frac{-9+\sqrt{93}}{2}
$