Y=3x^2+x-6

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

=3Y^2+Y-6

We move all terms to the left:

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

We get rid of parentheses

-3Y^2-Y+6=0

We add all the numbers together, and all the variables

-3Y^2-1Y+6=0

a = -3; b = -1; c = +6;
Δ = b2-4ac
Δ = -12-4·(-3)·6
Δ = 73
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{-(-1)-\sqrt{73}}{2*-3}=\frac{1-\sqrt{73}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*-3}=\frac{1+\sqrt{73}}{-6}
$