X+1/2x=-12

Solution for X+1/2x=-12 equation:

X+1/2X=-12

We move all terms to the left:

X+1/2X-(-12)=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+12=0

We multiply all the terms by the denominator


X*2X+12*2X+1=0

Wy multiply elements

2X^2+24X+1=0

a = 2; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·2·1
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{142}}{2*2}=\frac{-24-2\sqrt{142}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{142}}{2*2}=\frac{-24+2\sqrt{142}}{4}
$