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19/11x+13x=209
We move all terms to the left:
19/11x+13x-(209)=0
Domain of the equation: 11x!=0We add all the numbers together, and all the variables
x!=0/11
x!=0
x∈R
13x+19/11x-209=0
We multiply all the terms by the denominator
13x*11x-209*11x+19=0
Wy multiply elements
143x^2-2299x+19=0
a = 143; b = -2299; c = +19;
Δ = b2-4ac
Δ = -22992-4·143·19
Δ = 5274533
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{-(-2299)-\sqrt{5274533}}{2*143}=\frac{2299-\sqrt{5274533}}{286} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2299)+\sqrt{5274533}}{2*143}=\frac{2299+\sqrt{5274533}}{286} $
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