x+8=-1/2x+5

Solution for x+8=-1/2x+5 equation:

x+8=-1/2x+5

We move all terms to the left:

x+8-(-1/2x+5)=0


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

x+1/2x-5+8=0

We multiply all the terms by the denominator


x*2x-5*2x+8*2x+1=0

Wy multiply elements

2x^2-10x+16x+1=0

We add all the numbers together, and all the variables

2x^2+6x+1=0

a = 2; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·2·1
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{7}}{2*2}=\frac{-6-2\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*2}=\frac{-6+2\sqrt{7}}{4}
$