2(y+5)=5/2y

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

2(y+5)=5/2y

We move all terms to the left:

2(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

2(y+5)-(+5/2y)=0

We multiply parentheses

2y-(+5/2y)+10=0

We get rid of parentheses

2y-5/2y+10=0

We multiply all the terms by the denominator


2y*2y+10*2y-5=0

Wy multiply elements

4y^2+20y-5=0

a = 4; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·4·(-5)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{30}}{2*4}=\frac{-20-4\sqrt{30}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{30}}{2*4}=\frac{-20+4\sqrt{30}}{8}
$