x+1/2x=495

Solution for x+1/2x=495 equation:

x+1/2x=495

We move all terms to the left:

x+1/2x-(495)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-495*2x+1=0

Wy multiply elements

2x^2-990x+1=0

a = 2; b = -990; c = +1;
Δ = b2-4ac
Δ = -9902-4·2·1
Δ = 980092
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:

$\sqrt{\Delta}=\sqrt{980092}=\sqrt{4*245023}=\sqrt{4}*\sqrt{245023}=2\sqrt{245023}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-2\sqrt{245023}}{2*2}=\frac{990-2\sqrt{245023}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+2\sqrt{245023}}{2*2}=\frac{990+2\sqrt{245023}}{4}
$