2y+1/2y+2=15

Solution for 2y+1/2y+2=15 equation:

2y+1/2y+2=15

We move all terms to the left:

2y+1/2y+2-(15)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

2y+1/2y-13=0

We multiply all the terms by the denominator


2y*2y-13*2y+1=0

Wy multiply elements

4y^2-26y+1=0

a = 4; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·4·1
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{165}}{2*4}=\frac{26-2\sqrt{165}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{165}}{2*4}=\frac{26+2\sqrt{165}}{8}
$