1/2x+x-60=600

Solution for 1/2x+x-60=600 equation:

1/2x+x-60=600

We move all terms to the left:

1/2x+x-60-(600)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-660=0

We multiply all the terms by the denominator


x*2x-660*2x+1=0

Wy multiply elements

2x^2-1320x+1=0

a = 2; b = -1320; c = +1;
Δ = b2-4ac
Δ = -13202-4·2·1
Δ = 1742392
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:

$\sqrt{\Delta}=\sqrt{1742392}=\sqrt{4*435598}=\sqrt{4}*\sqrt{435598}=2\sqrt{435598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1320)-2\sqrt{435598}}{2*2}=\frac{1320-2\sqrt{435598}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1320)+2\sqrt{435598}}{2*2}=\frac{1320+2\sqrt{435598}}{4}
$