9y^2=24y+16

Solution for 9y^2=24y+16 equation:

9y^2=24y+16

We move all terms to the left:

9y^2-(24y+16)=0

We get rid of parentheses

9y^2-24y-16=0

a = 9; b = -24; c = -16;
Δ = b2-4ac
Δ = -242-4·9·(-16)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{2}}{2*9}=\frac{24-24\sqrt{2}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*9}=\frac{24+24\sqrt{2}}{18}
$