7+3/y=y-6

Solution for 7+3/y=y-6 equation:

7+3/y=y-6

We move all terms to the left:

7+3/y-(y-6)=0


Domain of the equation: y!=0

y∈R


We get rid of parentheses

3/y-y+6+7=0

We multiply all the terms by the denominator


-y*y+6*y+7*y+3=0

We add all the numbers together, and all the variables

13y-y*y+3=0

Wy multiply elements

-1y^2+13y+3=0

a = -1; b = 13; c = +3;
Δ = b2-4ac
Δ = 132-4·(-1)·3
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{181}}{2*-1}=\frac{-13-\sqrt{181}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{181}}{2*-1}=\frac{-13+\sqrt{181}}{-2}
$