(y+1)(y-2)-3=0

Solution for (y+1)(y-2)-3=0 equation:

(y+1)(y-2)-3=0

We multiply parentheses ..

(+y^2-2y+y-2)-3=0

We get rid of parentheses

y^2-2y+y-2-3=0

We add all the numbers together, and all the variables

y^2-1y-5=0

a = 1; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·1·(-5)
Δ = 21
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{-(-1)-\sqrt{21}}{2*1}=\frac{1-\sqrt{21}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*1}=\frac{1+\sqrt{21}}{2}
$