y+5=5/2y

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-(+5/2y)+5=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}
$