11=3+30x-16x^2

Solution for 11=3+30x-16x^2 equation:

11=3+30x-16x^2

We move all terms to the left:

11-(3+30x-16x^2)=0

We get rid of parentheses

16x^2-30x-3+11=0

We add all the numbers together, and all the variables

16x^2-30x+8=0

a = 16; b = -30; c = +8;
Δ = b2-4ac
Δ = -302-4·16·8
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{97}}{2*16}=\frac{30-2\sqrt{97}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{97}}{2*16}=\frac{30+2\sqrt{97}}{32}
$