7y+8=1/5y

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

7y+8=1/5y

We move all terms to the left:

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


Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7y-1/5y+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

35y^2+40y-1=0

a = 35; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·35·(-1)
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{435}}{2*35}=\frac{-40-2\sqrt{435}}{70}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{435}}{2*35}=\frac{-40+2\sqrt{435}}{70}
$