-11y-2=5y^2

Solution for -11y-2=5y^2 equation:

-11y-2=5y^2

We move all terms to the left:

-11y-2-(5y^2)=0

determiningTheFunctionDomain
-5y^2-11y-2=0

a = -5; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·(-5)·(-2)
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{-(-11)-9}{2*-5}=\frac{2}{-10}
=-1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*-5}=\frac{20}{-10}
=-2
$