2y=15-24y^2

Solution for 2y=15-24y^2 equation:

2y=15-24y^2

We move all terms to the left:

2y-(15-24y^2)=0

We get rid of parentheses

24y^2+2y-15=0

a = 24; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·24·(-15)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*24}=\frac{-40}{48}
=-5/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*24}=\frac{36}{48}
=3/4
$