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4x+1/2x+2=128
We move all terms to the left:
4x+1/2x+2-(128)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
4x+1/2x-126=0
We multiply all the terms by the denominator
4x*2x-126*2x+1=0
Wy multiply elements
8x^2-252x+1=0
a = 8; b = -252; c = +1;
Δ = b2-4ac
Δ = -2522-4·8·1
Δ = 63472
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{63472}=\sqrt{16*3967}=\sqrt{16}*\sqrt{3967}=4\sqrt{3967}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-4\sqrt{3967}}{2*8}=\frac{252-4\sqrt{3967}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+4\sqrt{3967}}{2*8}=\frac{252+4\sqrt{3967}}{16} $
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