x+1/2x=140

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

x+1/2x=140

We move all terms to the left:

x+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=0

Wy multiply elements

2x^2-280x+1=0

a = 2; b = -280; c = +1;
Δ = b2-4ac
Δ = -2802-4·2·1
Δ = 78392
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:

$\sqrt{\Delta}=\sqrt{78392}=\sqrt{4*19598}=\sqrt{4}*\sqrt{19598}=2\sqrt{19598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-2\sqrt{19598}}{2*2}=\frac{280-2\sqrt{19598}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+2\sqrt{19598}}{2*2}=\frac{280+2\sqrt{19598}}{4}
$