Y=20w^2+27w+9

Solution for Y=20w^2+27w+9 equation:

=20Y^2+27Y+9

We move all terms to the left:

-(20Y^2+27Y+9)=0

We get rid of parentheses

-20Y^2-27Y-9=0

a = -20; b = -27; c = -9;
Δ = b2-4ac
Δ = -272-4·(-20)·(-9)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*-20}=\frac{24}{-40}
=-3/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*-20}=\frac{30}{-40}
=-3/4
$