X=-16x^2+55x+19

Solution for X=-16x^2+55x+19 equation:

X=-16X^2+55X+19

We move all terms to the left:

X-(-16X^2+55X+19)=0

We get rid of parentheses

16X^2-55X+X-19=0

We add all the numbers together, and all the variables

16X^2-54X-19=0

a = 16; b = -54; c = -19;
Δ = b2-4ac
Δ = -542-4·16·(-19)
Δ = 4132
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:

$\sqrt{\Delta}=\sqrt{4132}=\sqrt{4*1033}=\sqrt{4}*\sqrt{1033}=2\sqrt{1033}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{1033}}{2*16}=\frac{54-2\sqrt{1033}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{1033}}{2*16}=\frac{54+2\sqrt{1033}}{32}
$