Y=4x2-24x+7

Solution for Y=4x2-24x+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 = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{29}}{2*-4}=\frac{-24-4\sqrt{29}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{29}}{2*-4}=\frac{-24+4\sqrt{29}}{-8}
$