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x+1/3x+16=49
We move all terms to the left:
x+1/3x+16-(49)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
x+1/3x-33=0
We multiply all the terms by the denominator
x*3x-33*3x+1=0
Wy multiply elements
3x^2-99x+1=0
a = 3; b = -99; c = +1;
Δ = b2-4ac
Δ = -992-4·3·1
Δ = 9789
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{-(-99)-\sqrt{9789}}{2*3}=\frac{99-\sqrt{9789}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{9789}}{2*3}=\frac{99+\sqrt{9789}}{6} $
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