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(+5y)-24=0

We multiply parentheses

45y^2-24=0

a = 45; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·45·(-24)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*45}=\frac{0-12\sqrt{30}}{90}
=-\frac{12\sqrt{30}}{90}
=-\frac{2\sqrt{30}}{15}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*45}=\frac{0+12\sqrt{30}}{90}
=\frac{12\sqrt{30}}{90}
=\frac{2\sqrt{30}}{15}
$