x=120-1/2x

Solution for x=120-1/2x equation:

x=120-1/2x

We move all terms to the left:

x-(120-1/2x)=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+120)=0

We get rid of parentheses

x+1/2x-120=0

We multiply all the terms by the denominator


x*2x-120*2x+1=0

Wy multiply elements

2x^2-240x+1=0

a = 2; b = -240; c = +1;
Δ = b2-4ac
Δ = -2402-4·2·1
Δ = 57592
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:

$\sqrt{\Delta}=\sqrt{57592}=\sqrt{4*14398}=\sqrt{4}*\sqrt{14398}=2\sqrt{14398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14398}}{2*2}=\frac{240-2\sqrt{14398}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14398}}{2*2}=\frac{240+2\sqrt{14398}}{4}
$