(y+5)=5/2y

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Solution for (y+5)=5/2y equation:



(y+5)=5/2y
We move all terms to the left:
(y+5)-(5/2y)=0
Domain of the equation: 2y)!=0
y!=0/1
y!=0
y∈R
We add all the numbers together, and all the variables
(y+5)-(+5/2y)=0
We get rid of parentheses
y-5/2y+5=0
We multiply all the terms by the denominator
y*2y+5*2y-5=0
Wy multiply elements
2y^2+10y-5=0
a = 2; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·2·(-5)
Δ = 140
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{35}}{2*2}=\frac{-10-2\sqrt{35}}{4} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{35}}{2*2}=\frac{-10+2\sqrt{35}}{4} $

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