x+1/2x=48

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Solution for x+1/2x=48 equation:



x+1/2x=48
We move all terms to the left:
x+1/2x-(48)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We multiply all the terms by the denominator
x*2x-48*2x+1=0
Wy multiply elements
2x^2-96x+1=0
a = 2; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·2·1
Δ = 9208
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:
$\sqrt{\Delta}=\sqrt{9208}=\sqrt{4*2302}=\sqrt{4}*\sqrt{2302}=2\sqrt{2302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2302}}{2*2}=\frac{96-2\sqrt{2302}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2302}}{2*2}=\frac{96+2\sqrt{2302}}{4} $

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