-x+4=1/2x+2

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

-x+4=1/2x+2

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·(-2)·(-1)
Δ = 8
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:

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