x+1/2x=147

Solution for x+1/2x=147 equation:

x+1/2x=147

We move all terms to the left:

x+1/2x-(147)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-147*2x+1=0

Wy multiply elements

2x^2-294x+1=0

a = 2; b = -294; c = +1;
Δ = b2-4ac
Δ = -2942-4·2·1
Δ = 86428
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:

$\sqrt{\Delta}=\sqrt{86428}=\sqrt{4*21607}=\sqrt{4}*\sqrt{21607}=2\sqrt{21607}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-2\sqrt{21607}}{2*2}=\frac{294-2\sqrt{21607}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+2\sqrt{21607}}{2*2}=\frac{294+2\sqrt{21607}}{4}
$