14=2+29x-16x^2

Solution for 14=2+29x-16x^2 equation:

14=2+29x-16x^2

We move all terms to the left:

14-(2+29x-16x^2)=0

We get rid of parentheses

16x^2-29x-2+14=0

We add all the numbers together, and all the variables

16x^2-29x+12=0

a = 16; b = -29; c = +12;
Δ = b2-4ac
Δ = -292-4·16·12
Δ = 73
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{-(-29)-\sqrt{73}}{2*16}=\frac{29-\sqrt{73}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{73}}{2*16}=\frac{29+\sqrt{73}}{32}
$