80/x+11x=98

Solution for 80/x+11x=98 equation:

80/x+11x=98

We move all terms to the left:

80/x+11x-(98)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

11x+80/x-98=0

We multiply all the terms by the denominator


11x*x-98*x+80=0

We add all the numbers together, and all the variables

-98x+11x*x+80=0

Wy multiply elements

11x^2-98x+80=0

a = 11; b = -98; c = +80;
Δ = b2-4ac
Δ = -982-4·11·80
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-78}{2*11}=\frac{20}{22}
=10/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+78}{2*11}=\frac{176}{22}
=8
$