1.5=-16x^2+144x+128

Solution for 1.5=-16x^2+144x+128 equation:

1.5=-16x^2+144x+128

We move all terms to the left:

1.5-(-16x^2+144x+128)=0

We get rid of parentheses

16x^2-144x-128+1.5=0

We add all the numbers together, and all the variables

16x^2-144x-126.5=0

a = 16; b = -144; c = -126.5;
Δ = b2-4ac
Δ = -1442-4·16·(-126.5)
Δ = 28832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28832}=\sqrt{16*1802}=\sqrt{16}*\sqrt{1802}=4\sqrt{1802}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1802}}{2*16}=\frac{144-4\sqrt{1802}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1802}}{2*16}=\frac{144+4\sqrt{1802}}{32}
$