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2x+x+1/2x=84
We move all terms to the left:
2x+x+1/2x-(84)=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-84=0
We multiply all the terms by the denominator
3x*2x-84*2x+1=0
Wy multiply elements
6x^2-168x+1=0
a = 6; b = -168; c = +1;
Δ = b2-4ac
Δ = -1682-4·6·1
Δ = 28200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28200}=\sqrt{100*282}=\sqrt{100}*\sqrt{282}=10\sqrt{282}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-10\sqrt{282}}{2*6}=\frac{168-10\sqrt{282}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+10\sqrt{282}}{2*6}=\frac{168+10\sqrt{282}}{12} $
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