-16(t-1.5)(t+1)=14

Solution for -16(t-1.5)(t+1)=14 equation:

-16(t-1.5)(t+1)=14

We move all terms to the left:

-16(t-1.5)(t+1)-(14)=0

We multiply parentheses ..

-16(+t^2+t-1.5t-1.5)-14=0

We multiply parentheses

-16t^2-16t+16t+24-14=0

We add all the numbers together, and all the variables

-16t^2+10=0

a = -16; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-16)·10
Δ = 640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-16}=\frac{0-8\sqrt{10}}{-32}
=-\frac{8\sqrt{10}}{-32}
=-\frac{\sqrt{10}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-16}=\frac{0+8\sqrt{10}}{-32}
=\frac{8\sqrt{10}}{-32}
=\frac{\sqrt{10}}{-4}
$