x+9/2x=16

Solution for x+9/2x=16 equation:

x+9/2x=16

We move all terms to the left:

x+9/2x-(16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-16*2x+9=0

Wy multiply elements

2x^2-32x+9=0

a = 2; b = -32; c = +9;
Δ = b2-4ac
Δ = -322-4·2·9
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{238}}{2*2}=\frac{32-2\sqrt{238}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{238}}{2*2}=\frac{32+2\sqrt{238}}{4}
$