-1/2x+1=-x-8

Solution for -1/2x+1=-x-8 equation:

-1/2x+1=-x-8

We move all terms to the left:

-1/2x+1-(-x-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

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

We get rid of parentheses

-1/2x+1x+8+1=0

We multiply all the terms by the denominator


1x*2x+8*2x+1*2x-1=0

Wy multiply elements

2x^2+16x+2x-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 = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{83}}{2*2}=\frac{-18-2\sqrt{83}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{83}}{2*2}=\frac{-18+2\sqrt{83}}{4}
$