17=7+27x-16x^2

Solution for 17=7+27x-16x^2 equation:

17=7+27x-16x^2

We move all terms to the left:

17-(7+27x-16x^2)=0

We get rid of parentheses

16x^2-27x-7+17=0

We add all the numbers together, and all the variables

16x^2-27x+10=0

a = 16; b = -27; c = +10;
Δ = b2-4ac
Δ = -272-4·16·10
Δ = 89
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{-(-27)-\sqrt{89}}{2*16}=\frac{27-\sqrt{89}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{89}}{2*16}=\frac{27+\sqrt{89}}{32}
$