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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2+2x^2-30x-50x-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}
$