-12x+x+x+1/2x=360

Solution for -12x+x+x+1/2x=360 equation:

-12x+x+x+1/2x=360

We move all terms to the left:

-12x+x+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

-10x+1/2x-360=0

We multiply all the terms by the denominator


-10x*2x-360*2x+1=0

Wy multiply elements

-20x^2-720x+1=0

a = -20; b = -720; c = +1;
Δ = b2-4ac
Δ = -7202-4·(-20)·1
Δ = 518480
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:

$\sqrt{\Delta}=\sqrt{518480}=\sqrt{16*32405}=\sqrt{16}*\sqrt{32405}=4\sqrt{32405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32405}}{2*-20}=\frac{720-4\sqrt{32405}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32405}}{2*-20}=\frac{720+4\sqrt{32405}}{-40}
$