X=-16x^2+19x+1

Solution for X=-16x^2+19x+1 equation:

X=-16X^2+19X+1

We move all terms to the left:

X-(-16X^2+19X+1)=0

We get rid of parentheses

16X^2-19X+X-1=0

We add all the numbers together, and all the variables

16X^2-18X-1=0

a = 16; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·16·(-1)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{97}}{2*16}=\frac{18-2\sqrt{97}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{97}}{2*16}=\frac{18+2\sqrt{97}}{32}
$