X=-16x^2+27x+3

Solution for X=-16x^2+27x+3 equation:

X=-16X^2+27X+3

We move all terms to the left:

X-(-16X^2+27X+3)=0

We get rid of parentheses

16X^2-27X+X-3=0

We add all the numbers together, and all the variables

16X^2-26X-3=0

a = 16; b = -26; c = -3;
Δ = b2-4ac
Δ = -262-4·16·(-3)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{217}}{2*16}=\frac{26-2\sqrt{217}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{217}}{2*16}=\frac{26+2\sqrt{217}}{32}
$