Y=-8x^2-16x+42

Solution for Y=-8x^2-16x+42 equation:

=-8Y^2-16Y+42

We move all terms to the left:

-(-8Y^2-16Y+42)=0

We get rid of parentheses

8Y^2+16Y-42=0

a = 8; b = 16; c = -42;
Δ = b2-4ac
Δ = 162-4·8·(-42)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-40}{2*8}=\frac{-56}{16}
=-3+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+40}{2*8}=\frac{24}{16}
=1+1/2
$