-x-(1/2x)=9

Solution for -x-(1/2x)=9 equation:

-x-(1/2x)=9

We move all terms to the left:

-x-(1/2x)-(9)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+1/2x)-9=0

We add all the numbers together, and all the variables

-1x-(+1/2x)-9=0

We get rid of parentheses

-1x-1/2x-9=0

We multiply all the terms by the denominator


-1x*2x-9*2x-1=0

Wy multiply elements

-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}
$