9y^2=24-19y

Solution for 9y^2=24-19y equation:

9y^2=24-19y

We move all terms to the left:

9y^2-(24-19y)=0

We add all the numbers together, and all the variables

9y^2-(-19y+24)=0

We get rid of parentheses

9y^2+19y-24=0

a = 9; b = 19; c = -24;
Δ = b2-4ac
Δ = 192-4·9·(-24)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-35}{2*9}=\frac{-54}{18}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+35}{2*9}=\frac{16}{18}
=8/9
$