(Y+5)+(y+5)=5/2y

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

(+5)+(Y+5)=5/2Y

We move all terms to the left:

(+5)+(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)+5=0

We get rid of parentheses

Y-5/2Y+5+5=0

We multiply all the terms by the denominator


Y*2Y+5*2Y+5*2Y-5=0

Wy multiply elements

2Y^2+10Y+10Y-5=0

We add all the numbers together, and all the variables

2Y^2+20Y-5=0

a = 2; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·2·(-5)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{110}}{2*2}=\frac{-20-2\sqrt{110}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{110}}{2*2}=\frac{-20+2\sqrt{110}}{4}
$