X+1/2y=-8

Solution for X+1/2y=-8 equation:

X+1/2X=-8

We move all terms to the left:

X+1/2X-(-8)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+1/2X+8=0

We multiply all the terms by the denominator


X*2X+8*2X+1=0

Wy multiply elements

2X^2+16X+1=0

a = 2; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·2·1
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{62}}{2*2}=\frac{-16-2\sqrt{62}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{62}}{2*2}=\frac{-16+2\sqrt{62}}{4}
$