2/y+5=7y-3

Solution for 2/y+5=7y-3 equation:

2/y+5=7y-3

We move all terms to the left:

2/y+5-(7y-3)=0


Domain of the equation: y!=0

y∈R


We get rid of parentheses

2/y-7y+3+5=0

We multiply all the terms by the denominator


-7y*y+3*y+5*y+2=0

We add all the numbers together, and all the variables

8y-7y*y+2=0

Wy multiply elements

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

a = -7; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-7)·2
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{30}}{2*-7}=\frac{-8-2\sqrt{30}}{-14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{30}}{2*-7}=\frac{-8+2\sqrt{30}}{-14}
$