x+5=14-(1/2x)

Solution for x+5=14-(1/2x) equation:

x+5=14-(1/2x)

We move all terms to the left:

x+5-(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-(14-(+1/2x))+5=0

We multiply all the terms by the denominator


x*2x))-(14-(+5*2x))+1=0

Wy multiply elements

2x^2+10x=0

a = 2; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·2·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*2}=\frac{0}{4}
=0
$