Y=3x2-24x-7

Solution for Y=3x2-24x-7 equation:

=3Y^2-24Y-7

We move all terms to the left:

-(3Y^2-24Y-7)=0

We get rid of parentheses

-3Y^2+24Y+7=0

a = -3; b = 24; c = +7;
Δ = b2-4ac
Δ = 242-4·(-3)·7
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{165}}{2*-3}=\frac{-24-2\sqrt{165}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{165}}{2*-3}=\frac{-24+2\sqrt{165}}{-6}
$