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3x+1/2x=21
We move all terms to the left:
3x+1/2x-(21)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
3x*2x-21*2x+1=0
Wy multiply elements
6x^2-42x+1=0
a = 6; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·6·1
Δ = 1740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{435}}{2*6}=\frac{42-2\sqrt{435}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{435}}{2*6}=\frac{42+2\sqrt{435}}{12} $
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