x+9/11x=80

Solution for x+9/11x=80 equation:

x+9/11x=80

We move all terms to the left:

x+9/11x-(80)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We multiply all the terms by the denominator


x*11x-80*11x+9=0

Wy multiply elements

11x^2-880x+9=0

a = 11; b = -880; c = +9;
Δ = b2-4ac
Δ = -8802-4·11·9
Δ = 774004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{774004}=\sqrt{196*3949}=\sqrt{196}*\sqrt{3949}=14\sqrt{3949}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-880)-14\sqrt{3949}}{2*11}=\frac{880-14\sqrt{3949}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-880)+14\sqrt{3949}}{2*11}=\frac{880+14\sqrt{3949}}{22}
$