Y=4x^2+24x-23

Solution for Y=4x^2+24x-23 equation:

=4Y^2+24Y-23

We move all terms to the left:

-(4Y^2+24Y-23)=0

We get rid of parentheses

-4Y^2-24Y+23=0

a = -4; b = -24; c = +23;
Δ = b2-4ac
Δ = -242-4·(-4)·23
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{59}}{2*-4}=\frac{24-4\sqrt{59}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{59}}{2*-4}=\frac{24+4\sqrt{59}}{-8}
$