9y(4y-y)=24

Solution for 9y(4y-y)=24 equation:

9y(4y-y)=24

We move all terms to the left:

9y(4y-y)-(24)=0

We add all the numbers together, and all the variables

9y(+3y)-24=0

We multiply parentheses

27y^2-24=0

a = 27; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·27·(-24)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*27}=\frac{0-36\sqrt{2}}{54}
=-\frac{36\sqrt{2}}{54}
=-\frac{2\sqrt{2}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*27}=\frac{0+36\sqrt{2}}{54}
=\frac{36\sqrt{2}}{54}
=\frac{2\sqrt{2}}{3}
$