y=2y+5/4y+8

Solution for y=2y+5/4y+8 equation:

y=2y+5/4y+8

We move all terms to the left:

y-(2y+5/4y+8)=0


Domain of the equation: 4y+8)!=0

y∈R


We get rid of parentheses

y-2y-5/4y-8=0

We multiply all the terms by the denominator


y*4y-2y*4y-8*4y-5=0

Wy multiply elements

4y^2-8y^2-32y-5=0

We add all the numbers together, and all the variables

-4y^2-32y-5=0

a = -4; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·(-4)·(-5)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{59}}{2*-4}=\frac{32-4\sqrt{59}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{59}}{2*-4}=\frac{32+4\sqrt{59}}{-8}
$