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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-960x=0

a = 4; b = -960; c = 0;
Δ = b2-4ac
Δ = -9602-4·4·0
Δ = 921600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{921600}=960$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-960}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+960}{2*4}=\frac{1920}{8}
=240
$