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1/3x+2x=105
We move all terms to the left:
1/3x+2x-(105)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
2x+1/3x-105=0
We multiply all the terms by the denominator
2x*3x-105*3x+1=0
Wy multiply elements
6x^2-315x+1=0
a = 6; b = -315; c = +1;
Δ = b2-4ac
Δ = -3152-4·6·1
Δ = 99201
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{-(-315)-\sqrt{99201}}{2*6}=\frac{315-\sqrt{99201}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-315)+\sqrt{99201}}{2*6}=\frac{315+\sqrt{99201}}{12} $
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