x+1/2x=162

Solution for x+1/2x=162 equation:

x+1/2x=162

We move all terms to the left:

x+1/2x-(162)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-162*2x+1=0

Wy multiply elements

2x^2-324x+1=0

a = 2; b = -324; c = +1;
Δ = b2-4ac
Δ = -3242-4·2·1
Δ = 104968
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:

$\sqrt{\Delta}=\sqrt{104968}=\sqrt{4*26242}=\sqrt{4}*\sqrt{26242}=2\sqrt{26242}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-2\sqrt{26242}}{2*2}=\frac{324-2\sqrt{26242}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+2\sqrt{26242}}{2*2}=\frac{324+2\sqrt{26242}}{4}
$