x+1/2x=464

Solution for x+1/2x=464 equation:

x+1/2x=464

We move all terms to the left:

x+1/2x-(464)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-464*2x+1=0

Wy multiply elements

2x^2-928x+1=0

a = 2; b = -928; c = +1;
Δ = b2-4ac
Δ = -9282-4·2·1
Δ = 861176
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:

$\sqrt{\Delta}=\sqrt{861176}=\sqrt{4*215294}=\sqrt{4}*\sqrt{215294}=2\sqrt{215294}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-928)-2\sqrt{215294}}{2*2}=\frac{928-2\sqrt{215294}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-928)+2\sqrt{215294}}{2*2}=\frac{928+2\sqrt{215294}}{4}
$