5y^2=16-24y

Solution for 5y^2=16-24y equation:

5y^2=16-24y

We move all terms to the left:

5y^2-(16-24y)=0

We add all the numbers together, and all the variables

5y^2-(-24y+16)=0

We get rid of parentheses

5y^2+24y-16=0

a = 5; b = 24; c = -16;
Δ = b2-4ac
Δ = 242-4·5·(-16)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{14}}{2*5}=\frac{-24-8\sqrt{14}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{14}}{2*5}=\frac{-24+8\sqrt{14}}{10}
$