-x=-2-4x-6-5/2x

Solution for -x=-2-4x-6-5/2x equation:

-x=-2-4x-6-5/2x

We move all terms to the left:

-x-(-2-4x-6-5/2x)=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-(-4x-5/2x-8)=0

We add all the numbers together, and all the variables

-1x-(-4x-5/2x-8)=0

We get rid of parentheses

-1x+4x+5/2x+8=0

We multiply all the terms by the denominator


-1x*2x+4x*2x+8*2x+5=0

Wy multiply elements

-2x^2+8x^2+16x+5=0

We add all the numbers together, and all the variables

6x^2+16x+5=0

a = 6; b = 16; c = +5;
Δ = b2-4ac
Δ = 162-4·6·5
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{34}}{2*6}=\frac{-16-2\sqrt{34}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{34}}{2*6}=\frac{-16+2\sqrt{34}}{12}
$