9y2-96y+24=0

Solution for 9y2-96y+24=0 equation:

9y^2-96y+24=0

a = 9; b = -96; c = +24;
Δ = b2-4ac
Δ = -962-4·9·24
Δ = 8352
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:

$\sqrt{\Delta}=\sqrt{8352}=\sqrt{144*58}=\sqrt{144}*\sqrt{58}=12\sqrt{58}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{58}}{2*9}=\frac{96-12\sqrt{58}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{58}}{2*9}=\frac{96+12\sqrt{58}}{18}
$