Y=3x^2-17x+20

Solution for Y=3x^2-17x+20 equation:

=3Y^2-17Y+20

We move all terms to the left:

-(3Y^2-17Y+20)=0

We get rid of parentheses

-3Y^2+17Y-20=0

a = -3; b = 17; c = -20;
Δ = b2-4ac
Δ = 172-4·(-3)·(-20)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*-3}=\frac{-24}{-6}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*-3}=\frac{-10}{-6}
=1+2/3
$