5/4y=8-y

Solution for 5/4y=8-y equation:

5/4y=8-y

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

5/4y-(-1y+8)=0

We get rid of parentheses

5/4y+1y-8=0

We multiply all the terms by the denominator


1y*4y-8*4y+5=0

Wy multiply elements

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}
$