Y=2x^2-24x-5

Solution for Y=2x^2-24x-5 equation:

=2Y^2-24Y-5

We move all terms to the left:

-(2Y^2-24Y-5)=0

We get rid of parentheses

-2Y^2+24Y+5=0

a = -2; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-2)·5
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{154}}{2*-2}=\frac{-24-2\sqrt{154}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{154}}{2*-2}=\frac{-24+2\sqrt{154}}{-4}
$