(1/2x)+(x-25)+(1/2x)+(x-15)+100=540

Solution for (1/2x)+(x-25)+(1/2x)+(x-15)+100=540 equation:

(1/2x)+(x-25)+(1/2x)+(x-15)+100=540

We move all terms to the left:

(1/2x)+(x-25)+(1/2x)+(x-15)+100-(540)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2x)+(x-25)+(+1/2x)+(x-15)+100-540=0

We add all the numbers together, and all the variables

(+1/2x)+(x-25)+(+1/2x)+(x-15)-440=0

We get rid of parentheses

1/2x+x+1/2x+x-25-15-440=0

We multiply all the terms by the denominator


x*2x+x*2x-25*2x-15*2x-440*2x+1+1=0

We add all the numbers together, and all the variables

x*2x+x*2x-25*2x-15*2x-440*2x+2=0

Wy multiply elements

2x^2+2x^2-50x-30x-880x+2=0

We add all the numbers together, and all the variables

4x^2-960x+2=0

a = 4; b = -960; c = +2;
Δ = b2-4ac
Δ = -9602-4·4·2
Δ = 921568
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:

$\sqrt{\Delta}=\sqrt{921568}=\sqrt{16*57598}=\sqrt{16}*\sqrt{57598}=4\sqrt{57598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-4\sqrt{57598}}{2*4}=\frac{960-4\sqrt{57598}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+4\sqrt{57598}}{2*4}=\frac{960+4\sqrt{57598}}{8}
$