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3x-51+1/2x=360
We move all terms to the left:
3x-51+1/2x-(360)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
3x+1/2x-411=0
We multiply all the terms by the denominator
3x*2x-411*2x+1=0
Wy multiply elements
6x^2-822x+1=0
a = 6; b = -822; c = +1;
Δ = b2-4ac
Δ = -8222-4·6·1
Δ = 675660
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{675660}=\sqrt{4*168915}=\sqrt{4}*\sqrt{168915}=2\sqrt{168915}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-822)-2\sqrt{168915}}{2*6}=\frac{822-2\sqrt{168915}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-822)+2\sqrt{168915}}{2*6}=\frac{822+2\sqrt{168915}}{12} $
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