1/2*x+1/48x=16

Solution for 1/2*x+1/48x=16 equation:

1/2x+1/48x=16

We move all terms to the left:

1/2x+1/48x-(16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 48x!=0

x!=0/48

x!=0

x∈R


We calculate fractions


48x/96x^2+2x/96x^2-16=0

We multiply all the terms by the denominator


48x+2x-16*96x^2=0

We add all the numbers together, and all the variables

50x-16*96x^2=0

Wy multiply elements

-1536x^2+50x=0

a = -1536; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-1536)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-1536}=\frac{-100}{-3072}
=25/768
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-1536}=\frac{0}{-3072}
=0
$