Y=-3x^2+17x-23

Solution for Y=-3x^2+17x-23 equation:

=-3Y^2+17Y-23

We move all terms to the left:

-(-3Y^2+17Y-23)=0

We get rid of parentheses

3Y^2-17Y+23=0

a = 3; b = -17; c = +23;
Δ = b2-4ac
Δ = -172-4·3·23
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{13}}{2*3}=\frac{17-\sqrt{13}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{13}}{2*3}=\frac{17+\sqrt{13}}{6}
$