480-x-1/2x=3x-60

Solution for 480-x-1/2x=3x-60 equation:

480-x-1/2x=3x-60

We move all terms to the left:

480-x-1/2x-(3x-60)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-1/2x-(3x-60)+480=0

We get rid of parentheses

-1x-1/2x-3x+60+480=0

We multiply all the terms by the denominator


-1x*2x-3x*2x+60*2x+480*2x-1=0

Wy multiply elements

-2x^2-6x^2+120x+960x-1=0

We add all the numbers together, and all the variables

-8x^2+1080x-1=0

a = -8; b = 1080; c = -1;
Δ = b2-4ac
Δ = 10802-4·(-8)·(-1)
Δ = 1166368
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:

$\sqrt{\Delta}=\sqrt{1166368}=\sqrt{16*72898}=\sqrt{16}*\sqrt{72898}=4\sqrt{72898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1080)-4\sqrt{72898}}{2*-8}=\frac{-1080-4\sqrt{72898}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1080)+4\sqrt{72898}}{2*-8}=\frac{-1080+4\sqrt{72898}}{-16}
$