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100+(x-25)+1/2x+(x-15)+1/2x=540
We move all terms to the left:
100+(x-25)+1/2x+(x-15)+1/2x-(540)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
(x-25)+1/2x+(x-15)+1/2x-440=0
We get rid of parentheses
x+1/2x+x+1/2x-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} $
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