(y+7)*(2-y)=6^2-9*6+30-3*2^2

Solution for (y+7)*(2-y)=6^2-9*6+30-3*2^2 equation:

(y+7)(2-y)=6^2-9*6+30-3*2^2

We move all terms to the left:

(y+7)(2-y)-(6^2-9*6+30-3*2^2)=0

We add all the numbers together, and all the variables

(y+7)(-1y+2)-(6^2-9*6+30-3*2^2)=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-1y^2+2y-7y+14)=0

We get rid of parentheses

-1y^2+2y-7y+14=0

We add all the numbers together, and all the variables

-1y^2-5y+14=0

a = -1; b = -5; c = +14;
Δ = b2-4ac
Δ = -52-4·(-1)·14
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*-1}=\frac{-4}{-2}
=+2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*-1}=\frac{14}{-2}
=-7
$