Y=4x^2-24x-7

Solution for Y=4x^2-24x-7 equation:

=4Y^2-24Y-7

We move all terms to the left:

-(4Y^2-24Y-7)=0

We get rid of parentheses

-4Y^2+24Y+7=0

a = -4; b = 24; c = +7;
Δ = b2-4ac
Δ = 242-4·(-4)·7
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{43}}{2*-4}=\frac{-24-4\sqrt{43}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{43}}{2*-4}=\frac{-24+4\sqrt{43}}{-8}
$