x+4=14-1/2x

Solution for x+4=14-1/2x equation:

x+4=14-1/2x

We move all terms to the left:

x+4-(14-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-1/2x+14)+4=0

We get rid of parentheses

x+1/2x-14+4=0

We multiply all the terms by the denominator


x*2x-14*2x+4*2x+1=0

Wy multiply elements

2x^2-28x+8x+1=0

We add all the numbers together, and all the variables

2x^2-20x+1=0

a = 2; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·2·1
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-14\sqrt{2}}{2*2}=\frac{20-14\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+14\sqrt{2}}{2*2}=\frac{20+14\sqrt{2}}{4}
$