0=-24-8x+16x^2

Solution for 0=-24-8x+16x^2 equation:

0=-24-8x+16x^2

We move all terms to the left:

0-(-24-8x+16x^2)=0

We add all the numbers together, and all the variables

-(-24-8x+16x^2)=0

We get rid of parentheses

-16x^2+8x+24=0

a = -16; b = 8; c = +24;
Δ = b2-4ac
Δ = 82-4·(-16)·24
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-40}{2*-16}=\frac{-48}{-32}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+40}{2*-16}=\frac{32}{-32}
=-1
$