-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

-1x-1/2x-7=0

We multiply all the terms by the denominator


-1x*2x-7*2x-1=0

Wy multiply elements

-2x^2-14x-1=0

a = -2; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·(-2)·(-1)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{47}}{2*-2}=\frac{14-2\sqrt{47}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{47}}{2*-2}=\frac{14+2\sqrt{47}}{-4}
$