X+1/2y=16

Solution for X+1/2y=16 equation:

X+1/2X=16

We move all terms to the left:

X+1/2X-(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+1=0

Wy multiply elements

2X^2-32X+1=0

a = 2; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·2·1
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{254}}{2*2}=\frac{32-2\sqrt{254}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{254}}{2*2}=\frac{32+2\sqrt{254}}{4}
$