(9y^2+57y+44)=0

Solution for (9y^2+57y+44)=0 equation:

(9y^2+57y+44)=0

We get rid of parentheses

9y^2+57y+44=0

a = 9; b = 57; c = +44;
Δ = b2-4ac
Δ = 572-4·9·44
Δ = 1665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{185}}{2*9}=\frac{-57-3\sqrt{185}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{185}}{2*9}=\frac{-57+3\sqrt{185}}{18}
$