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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+2x-12x-1=0

We add all the numbers together, and all the variables

-4x^2-10x-1=0

a = -4; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-4)·(-1)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*-4}=\frac{10-2\sqrt{21}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*-4}=\frac{10+2\sqrt{21}}{-8}
$