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3x+122/5x=49
We move all terms to the left:
3x+122/5x-(49)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
3x*5x-49*5x+122=0
Wy multiply elements
15x^2-245x+122=0
a = 15; b = -245; c = +122;
Δ = b2-4ac
Δ = -2452-4·15·122
Δ = 52705
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{-(-245)-\sqrt{52705}}{2*15}=\frac{245-\sqrt{52705}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-245)+\sqrt{52705}}{2*15}=\frac{245+\sqrt{52705}}{30} $
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