x+1/2x+1/2x=140

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Solution for x+1/2x+1/2x=140 equation: 



x+1/2x+1/2x=140

We move all terms to the left:

x+1/2x+1/2x-(140)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We multiply all the terms by the denominator


x*2x-140*2x+1+1=0

We add all the numbers together, and all the variables

x*2x-140*2x+2=0

Wy multiply elements

2x^2-280x+2=0

a = 2; b = -280; c = +2;
Δ = b2-4ac
Δ = -2802-4·2·2
Δ = 78384
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:


$\sqrt{\Delta}=\sqrt{78384}=\sqrt{16*4899}=\sqrt{16}*\sqrt{4899}=4\sqrt{4899}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-4\sqrt{4899}}{2*2}=\frac{280-4\sqrt{4899}}{4}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+4\sqrt{4899}}{2*2}=\frac{280+4\sqrt{4899}}{4}
$

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