1/7y-8=-5y+28

Solution for 1/7y-8=-5y+28 equation:

1/7y-8=-5y+28

We move all terms to the left:

1/7y-8-(-5y+28)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We get rid of parentheses

1/7y+5y-28-8=0

We multiply all the terms by the denominator


5y*7y-28*7y-8*7y+1=0

Wy multiply elements

35y^2-196y-56y+1=0

We add all the numbers together, and all the variables

35y^2-252y+1=0

a = 35; b = -252; c = +1;
Δ = b2-4ac
Δ = -2522-4·35·1
Δ = 63364
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:

$\sqrt{\Delta}=\sqrt{63364}=\sqrt{4*15841}=\sqrt{4}*\sqrt{15841}=2\sqrt{15841}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-2\sqrt{15841}}{2*35}=\frac{252-2\sqrt{15841}}{70}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+2\sqrt{15841}}{2*35}=\frac{252+2\sqrt{15841}}{70}
$