X=-16t^2+110t+2

Solution for X=-16t^2+110t+2 equation:

X=-16X^2+110X+2

We move all terms to the left:

X-(-16X^2+110X+2)=0

We get rid of parentheses

16X^2-110X+X-2=0

We add all the numbers together, and all the variables

16X^2-109X-2=0

a = 16; b = -109; c = -2;
Δ = b2-4ac
Δ = -1092-4·16·(-2)
Δ = 12009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-\sqrt{12009}}{2*16}=\frac{109-\sqrt{12009}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+\sqrt{12009}}{2*16}=\frac{109+\sqrt{12009}}{32}
$