X+1/2x+x+1/2x=360

Solution for X+1/2x+x+1/2x=360 equation:

X+1/2X+X+1/2X=360

We move all terms to the left:

X+1/2X+X+1/2X-(360)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

2X+1/2X+1/2X-360=0

We multiply all the terms by the denominator


2X*2X-360*2X+1+1=0

We add all the numbers together, and all the variables

2X*2X-360*2X+2=0

Wy multiply elements

4X^2-720X+2=0

a = 4; b = -720; c = +2;
Δ = b2-4ac
Δ = -7202-4·4·2
Δ = 518368
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:

$\sqrt{\Delta}=\sqrt{518368}=\sqrt{16*32398}=\sqrt{16}*\sqrt{32398}=4\sqrt{32398}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32398}}{2*4}=\frac{720-4\sqrt{32398}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32398}}{2*4}=\frac{720+4\sqrt{32398}}{8}
$