(y+5)(y+5)-3=33

Solution for (y+5)(y+5)-3=33 equation:

(y+5)(y+5)-3=33

We move all terms to the left:

(y+5)(y+5)-3-(33)=0

We add all the numbers together, and all the variables

(y+5)(y+5)-36=0

We multiply parentheses ..

(+y^2+5y+5y+25)-36=0

We get rid of parentheses

y^2+5y+5y+25-36=0

We add all the numbers together, and all the variables

y^2+10y-11=0

a = 1; b = 10; c = -11;
Δ = b2-4ac
Δ = 102-4·1·(-11)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-12}{2*1}=\frac{-22}{2}
=-11
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+12}{2*1}=\frac{2}{2}
=1
$