0=3y^2-24y+45

Solution for 0=3y^2-24y+45 equation:

0=3y^2-24y+45

We move all terms to the left:

0-(3y^2-24y+45)=0

We add all the numbers together, and all the variables

-(3y^2-24y+45)=0

We get rid of parentheses

-3y^2+24y-45=0

a = -3; b = 24; c = -45;
Δ = b2-4ac
Δ = 242-4·(-3)·(-45)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6}{2*-3}=\frac{-30}{-6}
=+5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6}{2*-3}=\frac{-18}{-6}
=+3
$