Y=3x^2-2x-10

Solution for Y=3x^2-2x-10 equation:

=3Y^2-2Y-10

We move all terms to the left:

-(3Y^2-2Y-10)=0

We get rid of parentheses

-3Y^2+2Y+10=0

a = -3; b = 2; c = +10;
Δ = b2-4ac
Δ = 22-4·(-3)·10
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*-3}=\frac{-2-2\sqrt{31}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*-3}=\frac{-2+2\sqrt{31}}{-6}
$