-x-4(x+1)=1/2x+2

Solution for -x-4(x+1)=1/2x+2 equation:

-x-4(x+1)=1/2x+2

We move all terms to the left:

-x-4(x+1)-(1/2x+2)=0


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

x∈R


We add all the numbers together, and all the variables

-1x-4(x+1)-(1/2x+2)=0

We multiply parentheses

-1x-4x-(1/2x+2)-4=0

We get rid of parentheses

-1x-4x-1/2x-2-4=0

We multiply all the terms by the denominator


-1x*2x-4x*2x-2*2x-4*2x-1=0

Wy multiply elements

-2x^2-8x^2-4x-8x-1=0

We add all the numbers together, and all the variables

-10x^2-12x-1=0

a = -10; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-10)·(-1)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{26}}{2*-10}=\frac{12-2\sqrt{26}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{26}}{2*-10}=\frac{12+2\sqrt{26}}{-20}
$