1/2x+1=-x+8

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

1/2x+1=-x+8

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-16x+2x+1=0

We add all the numbers together, and all the variables

2x^2-14x+1=0

a = 2; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·2·1
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{47}}{2*2}=\frac{14-2\sqrt{47}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{47}}{2*2}=\frac{14+2\sqrt{47}}{4}
$