X=125-1/2x

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Solution for X=125-1/2x equation:



X=125-1/2X
We move all terms to the left:
X-(125-1/2X)=0
Domain of the equation: 2X)!=0
X!=0/1
X!=0
X∈R
We add all the numbers together, and all the variables
X-(-1/2X+125)=0
We get rid of parentheses
X+1/2X-125=0
We multiply all the terms by the denominator
X*2X-125*2X+1=0
Wy multiply elements
2X^2-250X+1=0
a = 2; b = -250; c = +1;
Δ = b2-4ac
Δ = -2502-4·2·1
Δ = 62492
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:
$\sqrt{\Delta}=\sqrt{62492}=\sqrt{4*15623}=\sqrt{4}*\sqrt{15623}=2\sqrt{15623}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-2\sqrt{15623}}{2*2}=\frac{250-2\sqrt{15623}}{4} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+2\sqrt{15623}}{2*2}=\frac{250+2\sqrt{15623}}{4} $

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