7y-8y-2y(y-1)=-1

Solution for 7y-8y-2y(y-1)=-1 equation:

7y-8y-2y(y-1)=-1

We move all terms to the left:

7y-8y-2y(y-1)-(-1)=0

We add all the numbers together, and all the variables

-1y-2y(y-1)+1=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-2y^2+y+1=0

a = -2; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-2)·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-2}=\frac{-4}{-4}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-2}=\frac{2}{-4}
=-1/2
$