Y=3x^2-18x-10

Solution for Y=3x^2-18x-10 equation:

=3Y^2-18Y-10

We move all terms to the left:

-(3Y^2-18Y-10)=0

We get rid of parentheses

-3Y^2+18Y+10=0

a = -3; b = 18; c = +10;
Δ = b2-4ac
Δ = 182-4·(-3)·10
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{111}}{2*-3}=\frac{-18-2\sqrt{111}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{111}}{2*-3}=\frac{-18+2\sqrt{111}}{-6}
$