1/2x=10-x

Solution for 1/2x=10-x equation:

1/2x=10-x

We move all terms to the left:

1/2x-(10-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+10)=0

We get rid of parentheses

1/2x+1x-10=0

We multiply all the terms by the denominator


1x*2x-10*2x+1=0

Wy multiply elements

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}
$