x+1/2x=63

Solution for x+1/2x=63 equation:

x+1/2x=63

We move all terms to the left:

x+1/2x-(63)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-63*2x+1=0

Wy multiply elements

2x^2-126x+1=0

a = 2; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·2·1
Δ = 15868
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:

$\sqrt{\Delta}=\sqrt{15868}=\sqrt{4*3967}=\sqrt{4}*\sqrt{3967}=2\sqrt{3967}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3967}}{2*2}=\frac{126-2\sqrt{3967}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3967}}{2*2}=\frac{126+2\sqrt{3967}}{4}
$