y=(y-7)(y+1)

Solution for y=(y-7)(y+1) equation:

y=(y-7)(y+1)

We move all terms to the left:

y-((y-7)(y+1))=0

We multiply parentheses ..

-((+y^2+y-7y-7))+y=0


We calculate terms in parentheses: -((+y^2+y-7y-7)), so:

(+y^2+y-7y-7)

We get rid of parentheses

y^2+y-7y-7

We add all the numbers together, and all the variables

y^2-6y-7

Back to the equation:

-(y^2-6y-7)


We add all the numbers together, and all the variables

y-(y^2-6y-7)=0

We get rid of parentheses

-y^2+y+6y+7=0

We add all the numbers together, and all the variables

-1y^2+7y+7=0

a = -1; b = 7; c = +7;
Δ = b2-4ac
Δ = 72-4·(-1)·7
Δ = 77
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{-(7)-\sqrt{77}}{2*-1}=\frac{-7-\sqrt{77}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{77}}{2*-1}=\frac{-7+\sqrt{77}}{-2}
$