5(y+12)-17(2-y)/7y-1=8

Solution for 5(y+12)-17(2-y)/7y-1=8 equation:

5(y+12)-17(2-y)/7y-1=8

We move all terms to the left:

5(y+12)-17(2-y)/7y-1-(8)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

5(y+12)-17(-1y+2)/7y-1-8=0

We add all the numbers together, and all the variables

5(y+12)-17(-1y+2)/7y-9=0

We multiply parentheses

5y-17(-1y+2)/7y+60-9=0

We multiply all the terms by the denominator


5y*7y-17(-1y+2)+60*7y-9*7y=0

We multiply parentheses

5y*7y+17y+60*7y-9*7y-34=0

Wy multiply elements

35y^2+17y+420y-63y-34=0

We add all the numbers together, and all the variables

35y^2+374y-34=0

a = 35; b = 374; c = -34;
Δ = b2-4ac
Δ = 3742-4·35·(-34)
Δ = 144636
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:

$\sqrt{\Delta}=\sqrt{144636}=\sqrt{4*36159}=\sqrt{4}*\sqrt{36159}=2\sqrt{36159}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(374)-2\sqrt{36159}}{2*35}=\frac{-374-2\sqrt{36159}}{70}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(374)+2\sqrt{36159}}{2*35}=\frac{-374+2\sqrt{36159}}{70}
$