y=3y^2-17y+24

Solution for y=3y^2-17y+24 equation:

y=3y^2-17y+24

We move all terms to the left:

y-(3y^2-17y+24)=0

We get rid of parentheses

-3y^2+y+17y-24=0

We add all the numbers together, and all the variables

-3y^2+18y-24=0

a = -3; b = 18; c = -24;
Δ = b2-4ac
Δ = 182-4·(-3)·(-24)
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{-(18)-6}{2*-3}=\frac{-24}{-6}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*-3}=\frac{-12}{-6}
=+2
$