2y=1/2y+25.5

Solution for 2y=1/2y+25.5 equation:

2y=1/2y+25.5

We move all terms to the left:

2y-(1/2y+25.5)=0


Domain of the equation: 2y+25.5)!=0

y∈R


We get rid of parentheses

2y-1/2y-25.5=0

We multiply all the terms by the denominator


2y*2y-(25.5)*2y-1=0

We multiply parentheses

2y*2y-51y-1=0

Wy multiply elements

4y^2-51y-1=0

a = 4; b = -51; c = -1;
Δ = b2-4ac
Δ = -512-4·4·(-1)
Δ = 2617
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2617}}{2*4}=\frac{51-\sqrt{2617}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2617}}{2*4}=\frac{51+\sqrt{2617}}{8}
$