5/8y+8=5+1/2y

Solution for 5/8y+8=5+1/2y equation:

5/8y+8=5+1/2y

We move all terms to the left:

5/8y+8-(5+1/2y)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

5/8y-(1/2y+5)+8=0

We get rid of parentheses

5/8y-1/2y-5+8=0

We calculate fractions


10y/16y^2+(-8y)/16y^2-5+8=0

We add all the numbers together, and all the variables

10y/16y^2+(-8y)/16y^2+3=0

We multiply all the terms by the denominator


10y+(-8y)+3*16y^2=0

Wy multiply elements

48y^2+10y+(-8y)=0

We get rid of parentheses

48y^2+10y-8y=0

We add all the numbers together, and all the variables

48y^2+2y=0

a = 48; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·48·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*48}=\frac{-4}{96}
=-1/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*48}=\frac{0}{96}
=0
$