Y=-6x^2-15x+6

Solution for Y=-6x^2-15x+6 equation:

=-6Y^2-15Y+6

We move all terms to the left:

-(-6Y^2-15Y+6)=0

We get rid of parentheses

6Y^2+15Y-6=0

a = 6; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·6·(-6)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{41}}{2*6}=\frac{-15-3\sqrt{41}}{12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{41}}{2*6}=\frac{-15+3\sqrt{41}}{12}
$