Y=3x^2-23x+14

Solution for Y=3x^2-23x+14 equation:

=3Y^2-23Y+14

We move all terms to the left:

-(3Y^2-23Y+14)=0

We get rid of parentheses

-3Y^2+23Y-14=0

a = -3; b = 23; c = -14;
Δ = b2-4ac
Δ = 232-4·(-3)·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-19}{2*-3}=\frac{-42}{-6}
=+7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+19}{2*-3}=\frac{-4}{-6}
=2/3
$