2x+10/2=5/2x

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Solution for 2x+10/2=5/2x equation:



2x+10/2=5/2x
We move all terms to the left:
2x+10/2-(5/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2x-(+5/2x)+10/2=0
We add all the numbers together, and all the variables
2x-(+5/2x)+5=0
We get rid of parentheses
2x-5/2x+5=0
We multiply all the terms by the denominator
2x*2x+5*2x-5=0
Wy multiply elements
4x^2+10x-5=0
a = 4; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·4·(-5)
Δ = 180
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:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*4}=\frac{-10-6\sqrt{5}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*4}=\frac{-10+6\sqrt{5}}{8} $

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