.1/2x+8=14-x

Solution for .1/2x+8=14-x equation:

.1/2x+8=14-x

We move all terms to the left:

.1/2x+8-(14-x)=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+14)+8=0

We get rid of parentheses

.1/2x+1x-14+8=0

We multiply all the terms by the denominator


1x*2x-14*2x+8*2x+.1=0

We add all the numbers together, and all the variables

1x*2x-14*2x+8*2x+0.1=0

Wy multiply elements

2x^2-28x+16x+0.1=0

We add all the numbers together, and all the variables

2x^2-12x+0.1=0

a = 2; b = -12; c = +0.1;
Δ = b2-4ac
Δ = -122-4·2·0.1
Δ = 143.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-\sqrt{143.2}}{2*2}=\frac{12-\sqrt{143.2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+\sqrt{143.2}}{2*2}=\frac{12+\sqrt{143.2}}{4}
$