20y+y^2=-75

Solution for 20y+y^2=-75 equation:

20y+y^2=-75

We move all terms to the left:

20y+y^2-(-75)=0

We add all the numbers together, and all the variables

y^2+20y+75=0

a = 1; b = 20; c = +75;
Δ = b2-4ac
Δ = 202-4·1·75
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10}{2*1}=\frac{-30}{2}
=-15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10}{2*1}=\frac{-10}{2}
=-5
$