2x+500=2800+1/2x

Solution for 2x+500=2800+1/2x equation:

2x+500=2800+1/2x

We move all terms to the left:

2x+500-(2800+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

2x-(1/2x+2800)+500=0

We get rid of parentheses

2x-1/2x-2800+500=0

We multiply all the terms by the denominator


2x*2x-2800*2x+500*2x-1=0

Wy multiply elements

4x^2-5600x+1000x-1=0

We add all the numbers together, and all the variables

4x^2-4600x-1=0

a = 4; b = -4600; c = -1;
Δ = b2-4ac
Δ = -46002-4·4·(-1)
Δ = 21160016
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:

$\sqrt{\Delta}=\sqrt{21160016}=\sqrt{16*1322501}=\sqrt{16}*\sqrt{1322501}=4\sqrt{1322501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4600)-4\sqrt{1322501}}{2*4}=\frac{4600-4\sqrt{1322501}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4600)+4\sqrt{1322501}}{2*4}=\frac{4600+4\sqrt{1322501}}{8}
$