5+1/2y=3/8y+8

Solution for 5+1/2y=3/8y+8 equation:

5+1/2y=3/8y+8

We move all terms to the left:

5+1/2y-(3/8y+8)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

1/2y-3/8y-8+5=0

We calculate fractions


8y/16y^2+(-6y)/16y^2-8+5=0

We add all the numbers together, and all the variables

8y/16y^2+(-6y)/16y^2-3=0

We multiply all the terms by the denominator


8y+(-6y)-3*16y^2=0

Wy multiply elements

-48y^2+8y+(-6y)=0

We get rid of parentheses

-48y^2+8y-6y=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
$