Y=6x^2-17x-3

Solution for Y=6x^2-17x-3 equation:

=6Y^2-17Y-3

We move all terms to the left:

-(6Y^2-17Y-3)=0

We get rid of parentheses

-6Y^2+17Y+3=0

a = -6; b = 17; c = +3;
Δ = b2-4ac
Δ = 172-4·(-6)·3
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{-(17)-19}{2*-6}=\frac{-36}{-12}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+19}{2*-6}=\frac{2}{-12}
=-1/6
$