y/8y=20+3y

Solution for y/8y=20+3y equation:

y/8y=20+3y

We move all terms to the left:

y/8y-(20+3y)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

y/8y-(3y+20)=0

We get rid of parentheses

y/8y-3y-20=0

We multiply all the terms by the denominator


y-3y*8y-20*8y=0

Wy multiply elements

-24y^2+y-160y=0

We add all the numbers together, and all the variables

-24y^2-159y=0

a = -24; b = -159; c = 0;
Δ = b2-4ac
Δ = -1592-4·(-24)·0
Δ = 25281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25281}=159$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-159)-159}{2*-24}=\frac{0}{-48}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-159)+159}{2*-24}=\frac{318}{-48}
=-6+5/8
$