11x/x+3=8x-9/x+3

Solution for 11x/x+3=8x-9/x+3 equation:

11x/x+3=8x-9/x+3

We move all terms to the left:

11x/x+3-(8x-9/x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

11x/x-8x+9/x-3+3=0

We multiply all the terms by the denominator


11x-8x*x-3*x+3*x+9=0

We add all the numbers together, and all the variables

11x-8x*x+9=0

Wy multiply elements

-8x^2+11x+9=0

a = -8; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-8)·9
Δ = 409
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{-(11)-\sqrt{409}}{2*-8}=\frac{-11-\sqrt{409}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{409}}{2*-8}=\frac{-11+\sqrt{409}}{-16}
$