1/2x+1/2x+x-15+x-24+100=500

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Solution for 1/2x+1/2x+x-15+x-24+100=500 equation: 



1/2x+1/2x+x-15+x-24+100=500

We move all terms to the left:

1/2x+1/2x+x-15+x-24+100-(500)=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+1/2x-439=0

We multiply all the terms by the denominator


2x*2x-439*2x+1+1=0

We add all the numbers together, and all the variables

2x*2x-439*2x+2=0

Wy multiply elements

4x^2-878x+2=0

a = 4; b = -878; c = +2;
Δ = b2-4ac
Δ = -8782-4·4·2
Δ = 770852
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:


$\sqrt{\Delta}=\sqrt{770852}=\sqrt{4*192713}=\sqrt{4}*\sqrt{192713}=2\sqrt{192713}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-878)-2\sqrt{192713}}{2*4}=\frac{878-2\sqrt{192713}}{8}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-878)+2\sqrt{192713}}{2*4}=\frac{878+2\sqrt{192713}}{8}
$

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