1/2x+60=x

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Solution for 1/2x+60=x equation:



1/2x+60=x
We move all terms to the left:
1/2x+60-(x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+1/2x+60=0
We multiply all the terms by the denominator
-1x*2x+60*2x+1=0
Wy multiply elements
-2x^2+120x+1=0
a = -2; b = 120; c = +1;
Δ = b2-4ac
Δ = 1202-4·(-2)·1
Δ = 14408
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:
$\sqrt{\Delta}=\sqrt{14408}=\sqrt{4*3602}=\sqrt{4}*\sqrt{3602}=2\sqrt{3602}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3602}}{2*-2}=\frac{-120-2\sqrt{3602}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3602}}{2*-2}=\frac{-120+2\sqrt{3602}}{-4} $

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