27=-16x^2+40x+6

Solution for 27=-16x^2+40x+6 equation:

27=-16x^2+40x+6

We move all terms to the left:

27-(-16x^2+40x+6)=0

We get rid of parentheses

16x^2-40x-6+27=0

We add all the numbers together, and all the variables

16x^2-40x+21=0

a = 16; b = -40; c = +21;
Δ = b2-4ac
Δ = -402-4·16·21
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16}{2*16}=\frac{24}{32}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16}{2*16}=\frac{56}{32}
=1+3/4
$