-21y-5=4y^2

Solution for -21y-5=4y^2 equation:

-21y-5=4y^2

We move all terms to the left:

-21y-5-(4y^2)=0

determiningTheFunctionDomain
-4y^2-21y-5=0

a = -4; b = -21; c = -5;
Δ = b2-4ac
Δ = -212-4·(-4)·(-5)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-19}{2*-4}=\frac{2}{-8}
=-1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+19}{2*-4}=\frac{40}{-8}
=-5
$