1/2x+6=-x-3

Solution for 1/2x+6=-x-3 equation:

1/2x+6=-x-3

We move all terms to the left:

1/2x+6-(-x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1x-3)+6=0

We get rid of parentheses

1/2x+1x+3+6=0

We multiply all the terms by the denominator


1x*2x+3*2x+6*2x+1=0

Wy multiply elements

2x^2+6x+12x+1=0

We add all the numbers together, and all the variables

2x^2+18x+1=0

a = 2; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·2·1
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{79}}{2*2}=\frac{-18-2\sqrt{79}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{79}}{2*2}=\frac{-18+2\sqrt{79}}{4}
$