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

Solution for (y+7)(y-2)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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