X+2=-1/2x+8

Solution for X+2=-1/2x+8 equation:

X+2=-1/2X+8

We move all terms to the left:

X+2-(-1/2X+8)=0


Domain of the equation: 2X+8)!=0

X∈R


We get rid of parentheses

X+1/2X-8+2=0

We multiply all the terms by the denominator


X*2X-8*2X+2*2X+1=0

Wy multiply elements

2X^2-16X+4X+1=0

We add all the numbers together, and all the variables

2X^2-12X+1=0

a = 2; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·2·1
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{-(-12)-2\sqrt{34}}{2*2}=\frac{12-2\sqrt{34}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*2}=\frac{12+2\sqrt{34}}{4}
$