(-5y-2)(7-y)=9

Solution for (-5y-2)(7-y)=9 equation:

(-5y-2)(7-y)=9

We move all terms to the left:

(-5y-2)(7-y)-(9)=0

We add all the numbers together, and all the variables

(-5y-2)(-1y+7)-9=0

We multiply parentheses ..

(+5y^2-35y+2y-14)-9=0

We get rid of parentheses

5y^2-35y+2y-14-9=0

We add all the numbers together, and all the variables

5y^2-33y-23=0

a = 5; b = -33; c = -23;
Δ = b2-4ac
Δ = -332-4·5·(-23)
Δ = 1549
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{-(-33)-\sqrt{1549}}{2*5}=\frac{33-\sqrt{1549}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1549}}{2*5}=\frac{33+\sqrt{1549}}{10}
$