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3x+6x/97x=123
We move all terms to the left:
3x+6x/97x-(123)=0
Domain of the equation: 97x!=0We multiply all the terms by the denominator
x!=0/97
x!=0
x∈R
3x*97x+6x-123*97x=0
We add all the numbers together, and all the variables
6x+3x*97x-123*97x=0
Wy multiply elements
291x^2+6x-11931x=0
We add all the numbers together, and all the variables
291x^2-11925x=0
a = 291; b = -11925; c = 0;
Δ = b2-4ac
Δ = -119252-4·291·0
Δ = 142205625
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{142205625}=11925$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11925)-11925}{2*291}=\frac{0}{582} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11925)+11925}{2*291}=\frac{23850}{582} =40+95/97 $
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