7/y-7/(y-8)-8=0

Solution for 7/y-7/(y-8)-8=0 equation:

7/y-7/(y-8)-8=0


Domain of the equation: y!=0

y∈R



Domain of the equation: (y-8)!=0

We move all terms containing y to the left, all other terms to the right

y!=8

y∈R


We calculate fractions


(7y-56)/(y^2-8y)+(-7y)/(y^2-8y)-8=0

We multiply all the terms by the denominator


(7y-56)+(-7y)-8*(y^2-8y)=0

We multiply parentheses

-8y^2+(7y-56)+(-7y)+64y=0

We get rid of parentheses

-8y^2+7y-7y+64y-56=0

We add all the numbers together, and all the variables

-8y^2+64y-56=0

a = -8; b = 64; c = -56;
Δ = b2-4ac
Δ = 642-4·(-8)·(-56)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-48}{2*-8}=\frac{-112}{-16}
=+7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+48}{2*-8}=\frac{-16}{-16}
=1
$